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Yarra

Yarra may refer to:
 * Yarra River, a river in southern Victoria, Australia on which the city of Melbourne was founded
 * Yarra Trams, a public transport company specialising in trams in Melbourne, Australia
 * City of Yarra, a local government area in Victoria, Australia
 * South Yarra, a suburb of Melbourne, Victoria
 * Yarra, New South Wales, a locality near Goulburn, New South Wales
 * Yarra Creek, Tasmania, a locality
 * Division of Yarra, an abolished Australian federal electoral division
 * HMAS Yarra, name of Australian naval ships
 * Yarra Park, a park that surrounds the MCG and other ovals in Victoria (Australia).

 * See also
 * Jarrah (disambiguation)

title: Yarra


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Wikipedia:Selected anniversaries/April 8

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 * 217 – Roman emperor Caracalla (pictured) was assassinated near Harran and succeeded by his Praetorian Guard prefect Macrinus.
 * 876 – Abbasid forces decisively defeated the Saffarid emir Ya'qub ibn Laith, forcing the latter to halt his advance into Iraq.
 * 1630 – Kiliaen van Rensselaer purchased land near present-day Albany, New York, to establish Rensselaerswyck, which became the most successful patroonship under the Dutch West India Company.
 * 1820 – The Venus de Milo, an ancient Greek statue of a woman with its arms missing, was discovered on the island of Milos.
 * 1864 – American Civil War: Late-arriving reinforcements helped Confederate forces rout the Union Army at the Battle of Mansfield.
 * 1904 – Longacre Square in Midtown Manhattan was renamed Times Square after the New York Times building.
 * 1959 – A team of computer scientists and others met to discuss the creation of a common business-oriented programming language, which became COBOL.
 * 1942 – World War II: The United States Army Air Forces flew its first mission from India over the Hump (the eastern end of the Himalayas) to deliver materiel to China.
 * 1943 – Otto and Elise Hampel were executed in Berlin for performing acts of resistance against Nazism.
 * 1961 – A large explosion on board the MV Dara in the Persian Gulf killed 238 people.
 * 1968 – BOAC Flight 712 experienced an engine fire shortly after take-off from London Heathrow, leading to the deaths of five people on board, including flight attendant Jane Harrison, who was posthumously awarded a George Cross for heroism.
 * Born/died: | John II Komnenos |d|1143| Thomas of Tolentino |d|1321| John Clifford, 9th Baron Clifford |b|1435| Mary Stuart |b|1605| Niels Juel |d|1697|  Elizabeth Bacon Custer |b|1842| Allen Butler Talcott |b|1867| Marie Byles |b|1900| Betty Ford |b|1918| Sara Northrup Hollister |b|1924|  Kofi Annan |b|1938| Jack Tramiel |d|2012|

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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Wikipedia:Selected anniversaries/April 9

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 * 1917 – First World War: The Canadian Corps began the first wave of attacks of the Battle of Vimy Ridge in Vimy, France.
 * 1940 – World War II: During the German invasion of Norway, Vidkun Quisling attempted to seize power in the first coup to be broadcast over radio.
 * 1945 – The German heavy cruiser Admiral Scheer, the most successful capital-ship surface raider of the Second World War, was sunk by British bombers.
 * 1947 – Sixteen white and black men began a two-week journey in the American South, acting in defiance of local laws that enforced segregated seating on public buses.
 * 1947 – The Glazier–Higgins–Woodward tornadoes killed 181 people and injured 970 others in Texas, Oklahoma, and Kansas.
 * 1948 – Palestine war: Fighters from the Zionist paramilitary groups Irgun and Lehi attacked the village of Deir Yassin near Jerusalem, killing more than 100 Palestinian Arabs.
 * 1959 – NASA announced the selection of the Mercury Seven, the first astronauts in Project Mercury.
 * 1976 – The first EMD F40PH, Amtrak's most widespread diesel locomotive for many years, entered into service.
 * 1980 – Iraqi philosopher Muhammad Baqir al-Sadr (pictured) and his sister Amina were executed by the regime of Saddam Hussein.
 * 1993 – Iranian filmmaker Morteza Avini was killed by a land mine in Fakkeh while producing a documentary.
 * 1999 – Ibrahim Baré Maïnassara, President of Niger, was shot dead by soldiers in Niamey.
 * 2005 – Charles, Prince of Wales, married Camilla Parker Bowles in a civil ceremony at the Windsor Guildhall.
 * 2021 – Burmese military and police forces killed at least 82 civilians in the Bago massacre, including 2021 Myanmar coup d'état protesters.
 * Born/died:| Pope Benedict VIII |d|1024| Jean Quintin |d|1561| Henrik Rysensteen |b|1624| Samuel Fritz |b|1654| William Law |d|1761| Charles Proteus Steinmetz |b|1865| Jørn Utzon |b|1918| Alphonse Alley|b|1930|  Nate Colbert|b|1946| Vilhelm Bjerknes |d|1951| Natascha Engel |b|1967|  Peter Canavan |b|1971Jenna Jameson |b|1974| Jackie Evancho |b|2000| Nick Adenhart |d|2009 Nikki Grahame |d|2021| Nikki Grahame|d|2021|


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Wikipedia:Selected anniversaries/April 10

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 * 1221 — A Mongol army commanded by Tolui captured the city of Merv in present-day Turkmenistan, allegedly killing more than 1.7 million people.
 * 1724 Bach leads the first performance of his cantata Erfreut euch, ihr Herzen, BWV 66, his first cantata composed for Easter in Leipzig.
 * 1741 – War of the Austrian Succession: Prussian forces defeated Austrian troops at the Battle of Mollwitz in present-day Małujowice, Poland, cementing Frederick II's authority over the newly conquered territory of Silesia.
 * 1815 – Mount Tambora in Indonesia began the most powerful volcanic eruption in recorded history, killing at least 71,000 people and affecting temperatures worldwide.
 * 1858 – Big Ben, the bell in the Palace of Westminster's clock tower in London, was cast after the original bell cracked during testing.
 * 1919 – Mexican Revolution leader Emiliano Zapata (pictured) was shot to death near Ciudad Ayala, Morelos.
 * 1944 – The Holocaust: Slovak Jewish prisoners Rudolf Vrba and Alfréd Wetzler escaped from Auschwitz, later publishing a report that became one of the earliest and most detailed descriptions of the camp's mass killings.
 * 1963 – The U.S. Navy nuclear submarine USS Thresher (SSN-593) sank with all hands lost during deep-diving tests in the North Atlantic Ocean.
 * 1992 – First Nagorno-Karabakh War: Dozens of Armenian civilians were massacred in the village of Maraga by Azerbaijani forces.
 * Born/died: | Michael Tarchaniota Marullus |d|1500| Thomas Jones |d|1619| Wilhelm Egon von Fürstenberg |d|1704| Samuel Hahnemann |b|1755| Giovanni Aldini |b|1762| Kishori Amonkar |b|1932| Carol V. Robinson |b|1956| Carole Goble |b|1961| Stu Sutcliffe |d|1962| Evelyn Waugh |d|1966

April 10: Eid al-Fitr (Islam, 2024)

 * 1809 – Napoleonic Wars: The War of the Fifth Coalition began with the Austrian invasion of Bavaria, then a client state of France.
 * 1925 – The novel The Great Gatsby by American author F. Scott Fitzgerald was first published by Scribner's.
 * 1970 – In the midst of business disagreements with his bandmates, Paul McCartney announced his departure from the Beatles.
 * 1973 – In the deadliest aviation accident in Swiss history, Invicta International Airlines Flight 435 crashed into a hillside near Hochwald, killing 108 people of 145 on board.
 * 2019 – Scientists from the Event Horizon Telescope project released the first image of a black hole (depicted), located at the center of the galaxy M87.


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Wikipedia:Selected anniversaries/April 11

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 * 1241 – Mongol invasion of Europe: Mongol forces led by Batu Khan and Subutai defeated the army of King Béla IV at the Battle of Mohi near the river Sajó, a key victory in their first invasion of Hungary.
 * 1544 – Italian War of 1542–1546: French and Spanish forces fought a massive pitched battle in the Piedmont region of Italy.
 * 1713 – The main treaties of the Peace of Utrecht were signed in Utrecht in the Dutch Republic, helping to end the War of the Spanish Succession.
 * 1814 – The Treaty of Fontainebleau was signed, ending the War of the Sixth Coalition and forcing Napoleon to abdicate as ruler of France and sending him into exile on Elba.
 * 1888 – The Concertgebouw in Amsterdam, considered one of the world's finest concert halls, was inaugurated.
 * 1908 – Blücher, the last armored cruiser built by the Imperial German Navy, was launched.
 * 1913 – The cricket pavilion at the Nevill Ground was destroyed in an arson attack (damage pictured) that was attributed to militant suffragettes as part of a country-wide campaign co-ordinated by the Women's Social and Political Union.
 * 1919 – Paris Peace Conference: Woodrow Wilson overturns Japan's Racial Equality Proposal, stating that unanimous support was required.
 * 1921 – Emir Abdullah established the first centralised government in the recently created British protectorate of Transjordan.
 * 1963 – Pope John XXIII issued Pacem in terris, the first papal encyclical addressed to "all men of good will" rather than only to Catholics.
 * 1968 – Rudi Dutschke, the most prominent leader of the German student movement, survived an assassination attempt, which led to the largest protests to that date in Germany.
 * 1973 – On the Art of the Cinema, a treatise on film propaganda in support of the ruling Workers' Party of Korea written by the future North Korean leader Kim Jong Il, was published.
 * 1979 – Uganda–Tanzania War: The allied forces of Tanzania and the Uganda National Liberation Front captured the capital Kampala, deposing Ugandan president Idi Amin.
 * 1993 – Prisoners at the Southern Ohio Correctional Facility near Lucasville, Ohio, rioted and took over the prison for 11 days, resulting in the deaths of one officer and nine inmates.
 * 1996 – While attempting to set a record as the youngest person to pilot an airplane across the United States, the aircraft flown by seven-year-old Jessica Dubroff crashed in Cheyenne, Wyoming, killing her and two others.
 * 2002 – In a coup attempt, members of the Venezuelan military detained President Hugo Chávez and demanded his resignation.
 * 2011 – A bomb exploded at the central Oktyabrskaya station of the Minsk Metro in Belarus, killing 15 people and injuring more than 200.
 * 2017 – The tour bus of the German football team Borussia Dortmund was attacked with roadside bombs in Dortmund, killing a police officer and injuring one of the team's players.
 * 2023 – A Myanmar Air Force airstrike killed at least 100 villagers in Pazigyi.
 * Born/died:| Anawrahta |d|1077| | Stephen IV of Hungary |d|1165| Ramadan ibn Alauddin |d|1349| Edward Wightman |d|1612| Christopher Smart |b|1722| Edward Everett |b|1794| Ferdinand Lassalle |b|1825| John Douglas (English architect) |b|1830| Arthur Shrewsbury |b|1856| Charles Evans Hughes |b|1862| Joseph Merrick |d|1890| Percy Lavon Julian |b|1899| Percy Lavon Julian |b|1899| Bunny Ahearne |d|1985| Kurt Vonnegut |d|2007| Muhammad Kamaruzzaman |d|2015

April 11

 * 1689 – William III and Mary II (both pictured) were crowned joint sovereigns of England in a ceremony at Westminster Abbey.
 * 1809 – Napoleonic Wars: A hastily assembled Royal Navy fleet launched an assault against the main strength of the French Atlantic Fleet; an incomplete victory led to political turmoil in Britain.
 * 1951 – U.S. president Harry S. Truman relieved General of the Army Douglas MacArthur of his commands for making public statements about the Korean War that contradicted the administration's policies.
 * 2001 – In a FIFA World Cup qualifying match, Australia defeated American Samoa 31–0, the largest margin of victory recorded in international football.


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Wikipedia:Selected anniversaries/April 12

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 * 1204 – Troops of the Fourth Crusade entered Constantinople and began a sack of the city, temporarily dissolving the Byzantine Empire.
 * 1776 – American Revolution: The North Carolina Provincial Congress passed the Halifax Resolves, the first official action in the American colonies calling for independence from Great Britain.
 * 1822 – Greek War of Independence: Ottoman troops began a massacre of tens of thousands of Greeks (depicted) on the island of Chios.
 * 1861 – Confederate forces began a bombardment of Fort Sumter in the harbor of Charleston, South Carolina, starting the American Civil War.
 * 1910 – SMS Zrínyi, one of the last pre-dreadnoughts built by the Austro-Hungarian Navy, was launched in Trieste.
 * 1961 – Aboard Vostok 1, Soviet cosmonaut Yuri Gagarin performed the first human spaceflight, completing one orbit of Earth in 108 minutes.
 * 1980 – Samuel Doe took control of Liberia in a coup d'etat, overthrowing President William Tolbert and ending over 130 years of national democratic presidential succession.
 * 1980 – Canadian athlete Terry Fox embarked on an east-to-west "Marathon of Hope" from St. John's, Newfoundland and Labrador, with a prosthetic leg to raise funds for cancer research.
 * 1983 – Harold Washington was elected as the first African-American mayor of Chicago.
 * 2014 – A fire broke out in the hills near Valparaíso, Chile, eventually destroying at least 2,500 homes and leaving approximately 11,000 people homeless.
 * Born/died: | Richeza of Poland, Queen of Sweden |b|1116| Charles VII of Sweden |d|1167| Margaret of Bourbon, Queen of Navarre |d|1256| Nicola Amati |d|1684| George N. Briggs |b|1796| Peter Hesketh-Fleetwood |d|1866| Addie Joss |b|1880| Tenby Davies |b|1884| Imogen Holst |b|1907| Beverly Cleary |b|1916| Jane Withers |b|1926| Zelia Nuttall |d|1933| Sydney Allard |d|1966| Abbie Hoffman |d|1989| Xin Fengxia |d|1998


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Wikipedia:Selected anniversaries/April 13

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 * 1777 – American Revolutionary War: British and Hessian forces conducted a surprise attack against a Continental Army outpost at Bound Brook, New Jersey.
 * 1829 – The Roman Catholic Relief Act received royal assent, removing the most substantial restrictions on Catholics in the United Kingdom.
 * 1849 – During a closed session of the Diet of Hungary, Lajos Kossuth presented the Hungarian Declaration of Independence from the Habsburg monarchy.
 * 1942 – Austrian soldier Anton Schmid was executed for rescuing Jews from the Ponary massacre in Vilnius.
 * 1953 – Ian Fleming's novel Casino Royale was published as the first work to feature the British spy character James Bond.
 * 1953 – The CIA began Project MKUltra, an illegal, covert human research program into mind control.
 * 1956 – The Vietnamese National Army captured Ba Cụt, a military commander of the religious sect Hòa Hảo, which ran a de facto state in South Vietnam in opposition to Prime Minister Ngô Đình Diệm.
 * 1958 – In the midst of the Cold War, American pianist Van Cliburn won the inaugural International Tchaikovsky Competition in Moscow.
 * 1973 – Catch a Fire, the landmark reggae album by Bob Marley and the Wailers, was released.
 * 1976 – Forty people died in an explosion at an ammunition factory in Lapua, Finland.
 * 1997 – In golf, 21-year-old Tiger Woods became the youngest player to win the Masters Tournament, breaking the record for the lowest four-round score.
 * 2009 – Twenty-three people died in a fire at a homeless hostel (aftermath pictured) in Kamień Pomorski; it was Poland's deadliest fire since 1980.
 * Born/died: | Catherine de' Medici |b|1519| Arthur Herbert, 1st Earl of Torrington |d|1716| William Garrow |b|1760| Pierre Gaspard Chaumette |d|1794| Henry De la Beche |d|1855| Stanisław Ulam |b|1909| Stanley Donen |b|1924| Seamus Heaney |b|1939| Max Mosley |b|1940| Annie Jump Cannon |d|1941| Max Weinberg |b|1951| Abdul Salam Arif |d|1966| Danie Mellor |b|1971| Günter Grass |d|2015


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Wikipedia:Selected anniversaries/April 14

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 * 966 – Polish ruler Mieszko I converted to Christianity, an event considered to be the founding of the Polish state.
 * 1471 – Wars of the Roses: The Yorkists under Edward IV defeated the Lancastrians at the Battle of Barnet, killing Richard Neville, Earl of Warwick.
 * 1865 – Actor and Confederate sympathizer John Wilkes Booth fatally shot U.S. president Abraham Lincoln at Ford's Theatre in Washington, D.C.
 * 1906 – The Azusa Street Revival, the primary catalyst for the spread of Pentecostalism in the 20th century, opened in Los Angeles.
 * 1908 – The first Hauser Dam in the U.S. state of Montana failed, causing severe flooding and damage downstream.
 * 1909 – Following a reactionary military revolt against the Committee of Union and Progress, a mob began a massacre of Armenian Christians in the Adana Vilayet of the Ottoman Empire.
 * 1935 – Dust Bowl: A severe dust storm swept across Oklahoma and northern Texas, removing an estimated 300 million tons of topsoil from the prairies.
 * 1945 – World War II: The German town of Friesoythe was razed by the 4th Canadian Division on the orders of Major General Christopher Vokes.
 * 1967 – After leading a military coup three months earlier, Gnassingbé Eyadéma installed himself as President of Togo, a post that he held until 2005.
 * 1978 – Thousands of Georgians demonstrated in Tbilisi against an attempt by the Supreme Soviet of the Georgian SSR to change the constitutional status of the Georgian language.
 * 1999 – A storm dropped around 500,000 tonnes of hailstones on Sydney (examples pictured) and the east coast of New South Wales, causing about A$2.3 billion in damages, the costliest natural disaster in Australian insurance history.
 * 2010 – Nearly 2,700 people were killed in an earthquake registering 6.9 Mw in Yushu Tibetan Autonomous Prefecture, China.
 * 2014 – Boko Haram militants kidnapped 276 schoolgirls from a government secondary school in the town of Chibok, Nigeria.
 * Born/died this day: | Lucia Visconti |d|1424| Christiaan Huygens |b|1629| William Whitehead |d|1785| Harriett Ellen Grannis Arey |b|1819| Alexander Greenlaw Hamilton |b|1852| Princess Beatrice of the United Kingdom |b|1857| V. Gordon Childe |b|1892| L. L. Zamenhof |d|1917| Rod Steiger |b|1925| Berry Berenson |b|1948| Rachel Carson |d|1964| Lita |b|1975| Sarah Michelle Gellar |b|1977


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Wikipedia:Selected anniversaries/April 15

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 * 769 – The final session of the Lateran Council, convened to rectify abuses in the papal electoral process that had led to the elevation of the antipopes Constantine II and Philip, was held in Rome.
 * 1071 – Byzantine–Norman wars: After a siege of almost three years, Italo-Norman forces conquered the city of Bari, the capital of the Catepanate of Italy, ending more than five centuries of Byzantine presence in the region.
 * 1738 – Serse, an opera by Baroque composer George Frideric Handel loosely based on Xerxes I of Persia, premiered in London.
 * 1802 – English poet William Wordsworth and his sister Dorothy encountered a "long belt" of daffodils while walking around Ullswater in the Lake District, inspiring him to pen his best-known work, "I Wandered Lonely as a Cloud".
 * 1861 – The Italian tricolour is adopted as national flag by the newly formed Kingdom of Italy.
 * 1912 – More than 1,500 people on the Titanic died when the passenger liner sank after colliding with an iceberg southeast of Newfoundland.
 * 1922 – U.S. senator John B. Kendrick (pictured) introduced a resolution calling for an investigation of a secret land deal involving U.S. president Warren G. Harding's administration, leading to the Teapot Dome scandal.
 * 1927 – Torrential rains caused the Mississippi River to break out of its levee system in at least 145 places, resulting in the worst flooding in the history of the United States.
 * 1947 – Jackie Robinson, the first African American to break the baseball color line, played his first game in Major League Baseball.
 * 1952 – The Boeing B-52 Stratofortress, a long-range, subsonic, jet-powered, strategic bomber operated by the U.S. Air Force for most of the aircraft's history, made its first flight.
 * 1957 – The Indiaman departed Victoria Coach Station, London, as part of the first UK–India bus service.
 * 1958 – On Walter O'Malley initiative, the Los Angeles Dodgers and San Francisco Giants played the first Major League Baseball game on the U.S. West Coast.
 * 1994 – At a GATT ministerial meeting in Marrakesh, Morocco, representatives of 123 countries and the European Communities signed an agreement to establish the World Trade Organization.
 * 2013 – Dzhokhar and Tamerlan Tsarnaev set off two pressure cooker bombs during the running of the Boston Marathon, killing three people and injuring 264 others.
 * Born/died: | Richard Poore |d|1237| Guru Arjan |b|1563| Robert Persons |d|1610| George Calvert, 1st Baron Baltimore |d|1632| Leonhard Euler |b|1707| Mikhail Lomonosov |d|1765| Wilhelm Busch |b|1832| Stanley Bruce |b|1883| Richard von Weizsäcker |b|1920| Robert W. Gore |b|1937| Hugh Thompson Jr. |b|1943| Emma Thompson |b|1959| Carol W. Greider |b|1961| Arsenio Lacson |d|1962| Dara Torres |b|1967| Milton Bradley |b|1978| Seth Rogen |b|1982| Greta Garbo |d|1990


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Wikipedia:Selected anniversaries/April 16

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 * 1799 – French Revolutionary Wars: Severely outnumbered French forces repulsed an Ottoman attack at the Battle of Mount Tabor in present-day Israel.
 * 1912 – American pilot Harriet Quimby (pictured) became the first woman to fly across the English Channel.
 * 1917 – World War I: Several French army corps began a massive assault against the German-occupied Chemin des Dames ridge, south of Laon, France.
 * 1919 – Polish–Soviet War: The Polish army launched the Vilna offensive to capture Vilnius (now in Lithuania) from the Red Army.
 * 1963 – In response to an open letter written by white clergymen, Martin Luther King Jr. wrote the Letter from Birmingham Jail in defence of the strategy of nonviolent resistance against racism.
 * 2001 – India and Bangladesh began a six-day conflict over their disputed border, which ended in a stalemate.
 * 2007 – In one of the deadliest shooting incidents in United States history, a gunman killed 32 people and wounded over 20 more before committing suicide at the Virginia Polytechnic Institute and State University in Blacksburg, Virginia (memorial pictured).
 * Born/died: | Fructuosus of Braga |d|665| John Hastings, 2nd Earl of Pembroke |d|1375| Tabinshwehti |b|1516| Francisco Goya |d|1828| Harry Chauvel |b|1865| John Millington Synge |b|1871| Farran Zerbe |b|1871| Gertrude Chandler Warner |b|1890| William T. Stearn |b|1911|  Joan Bakewell |b|1933| Johnnie Lewis |b|1946| R. Carlos Nakai |b|1946| Yasunari Kawabata |d|1972| Khalil al-Wazir |d|1988| Johnny Peirson |d|2021

April 16

 * 1520 – A revolt of citizens in Toledo, Castile, opposed to the rule of the foreign-born Charles I began when the royal government attempted to unseat radical city councilors.
 * 1862 – Slavery in Washington, D.C., ended when the District of Columbia Compensated Emancipation Act became law.
 * 1945 – Second World War: British and Canadian forces concluded the Liberation of Arnhem in the Netherlands from German occupation.
 * 1948 – The Organisation for European Economic Co-operation, headquartered in Paris, was founded.
 * 2014 – The ferry MV Sewol (pictured) capsized and sank off Donggeochado, South Korea, killing 306 people, mainly students from Danwon High School.


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Wikipedia:Selected anniversaries/April 17

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 * 1080 – Canute IV became King of Denmark upon the death of his brother Harald III.
 * 1797 – French Revolutionary Wars: British forces commanded by Lieutenant-General Ralph Abercromby invaded the Spanish colonial port of San Juan, Puerto Rico.
 * 1907 – Minas Geraes (pictured), the first of three Brazilian dreadnought battleships, was laid down, sparking a vastly expensive South American naval arms race with Argentina and Chile.
 * 1951 – The Peak District was designated the first national park in the United Kingdom.
 * 1969 – Sirhan Sirhan was convicted of the assassination of United States Senator Robert F. Kennedy.
 * 1971 – Ustaše-affiliated Croatian separatists attacked the Yugoslav embassy in Stockholm, fatally shooting the ambassador, Vladimir Rolović.
 * 1975 – The Khmer Rouge captured Phnom Penh, the capital of the Khmer Republic, ending the Cambodian Civil War and establishing the socialist state of Democratic Kampuchea.
 * 1986 – Having supposedly been at war for 335 years without a single shot having been fired and no casualties incurred, the Netherlands and the Isles of Scilly declared peace.
 * 2014 – NASA announced the discovery of Kepler-186f, the first exoplanet with a radius similar to Earth's discovered in the habitable zone of another star.
 * Born/died: | Bernard of Italy |d|818| Marino Faliero |d|1355| Benjamin Franklin |d|1790| Mary Jefferson Eppes |d|1804| Hannah Webster Foster |d|1840| William R. Day |b|1849| Cap Anson |b|1852|Karen Blixen |b|1885| Neville McNamara |b|1923| Lucrețiu Pătrășcanu |d|1954| Elda Emma Anderson |d|1961| Vikram |b|1966 Victoria Beckham|b|1974

April 17: Evacuation Day in Syria (1946)

 * 1362 – Lithuanian Crusade: After a month-long siege, forces of the Teutonic Order captured and destroyed Kaunas Castle (reconstruction pictured), which was defended by troops of the Grand Duchy of Lithuania.
 * 1783 – The Mechanical Turk, a fraudulent chess-playing "machine" by Wolfgang von Kempelen that was secretly controlled by a hidden human, began a tour of Europe.
 * 1809 – Napoleonic Wars: After a three-day chase, the French ship D'Hautpoul was captured off Puerto Rico by a British squadron under Alexander Cochrane.
 * 1973 – George Lucas began writing a 13-page film treatment that later formed the basis of Star Wars.
 * 1984 – Metropolitan Police officer Yvonne Fletcher was shot and killed while on duty during a protest outside the Libyan embassy in London, resulting in an 11-day police siege of the building and a breakdown of Libya–United Kingdom relations.


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Wikipedia:Selected anniversaries/April 18

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 * 1689 – Glorious Revolution: Provincial militia and citizens in Boston revolted, arresting officials of the Dominion of New England.
 * 1864 – American Civil War: African-American Union soldiers were massacred and mutilated during and after the Battle of Poison Spring.
 * 1881 – The painted ceilings of the Natural History Museum, London, were unveiled when the building opened its doors to the public.
 * 1915 – World War I: Hit by ground fire, French aviation pioneer Roland Garros (pictured) landed his aircraft behind enemy lines and was taken prisoner.
 * 1949 – The Republic of Ireland Act 1948 came into force, declaring Ireland a republic and terminating its membership in the British Commonwealth of Nations.
 * 1958 – Controversial American poet Ezra Pound was released from St. Elizabeths Hospital, a psychiatric hospital in Washington, D.C., in which he had been incarcerated for twelve years.
 * 1996 – Operation Grapes of Wrath: Israeli forces shelled Qana, Lebanon, killing at least 100 civilians and injuring more than 110 others at a United Nations compound.
 * 2019 – The United States Department of Justice released a redacted version of the Mueller report about the investigation of Russian influence on the U.S. presidential election to Congress and the public.
 * Born/died: | Gratian |b|359| Ippolita Maria Sforza |b|1445 or 1446| Lucrezia Borgia |b|1480| John Leland |d|1552| Polydore Vergil |d|1555| Paul-Émile Lecoq de Boisbaudran |b|1838| Ludwig Levy |b|1854| Bertha Isaacs |b|1900| Pigmeat Markham |b|1904| Martha Ripley |d|1912| Gertrude Vanderbilt Whitney |d|1942| Albert Einstein |d|1955|Robert Christgau |b|1942


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Wikipedia:Selected anniversaries/April 19

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 * 1506 – In Lisbon, a crowd began a massacre of Jews who had been forced to convert to Christianity.
 * 1713 – With no living male heirs, Charles VI, Holy Roman Emperor, issued the Pragmatic Sanction, allowing the Habsburg hereditary possessions to be inherited by a daughter.
 * 1775 – The American Revolutionary War began with the Battles of Lexington and Concord in the British colony of Massachusetts.
 * 1782 – The States General of the Dutch Republic received John Adams, and the house he had purchased in The Hague became the first United States embassy.
 * 1903 – Anti-Jewish riots broke out in Kishinev, the capital of Bessarabia Governorate, causing the death of nearly 50 Jews and focusing worldwide attention on the persecution of Jews in Russia.
 * 1956 – American actress Grace Kelly (pictured) became the princess consort of Monaco upon her marriage to Rainier III.
 * 1971 – Salyut 1, the first space station, was launched from the Baikonur Cosmodrome near Tyuratam in the Soviet Union.
 * 1971 – The Doors' L.A. Woman was released, their final album during Jim Morrison's lifetime.
 * 1984 – "Advance Australia Fair", written by Scottish-born composer Peter Dodds McCormick, officially replaced "God Save the Queen" as Australia's national anthem.
 * 1995 – A car bombing destroyed much of the Alfred P. Murrah Federal Building in Oklahoma City, killing 168 people and injuring more than 680 others.
 * 2015 – Freddie Gray, a 25-year-old African American, died of injuries sustained while in the custody of the Baltimore Police Department.
 * Born/died: | Eanflæd |b|626| Jagat Gosain |d|1619| George St Lo |b|1655| Elizabeth Raffald |d|1781| Benjamin Rush |d|1813| Sydney Barnes |b|1873| Ernst Rüdin |b|1874| Benjamin Disraeli |d|1881| Jiroemon Kimura |b|1897| Glenn T. Seaborg |b|1912 Michel Roux |b|1941| Lo Kauppi |b|1970| Hermine Braunsteiner |d|1999| Aaron Hernandez |d|2017 |Kwon Ki-ok |d|1988}}


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Wikipedia:Selected anniversaries/April 20

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 * 1537 – Bacatá, the main settlement of the Muisca Confederation in present-day Colombia, was conquered by Spanish conquistadors led by Gonzalo Jiménez de Quesada.
 * 1657 – Anglo-Spanish War: The English navy sank much of a Spanish treasure fleet at the Battle of Santa Cruz de Tenerife off the Canary Islands, but was unable to capture the treasure.
 * 1809 – War of the Fifth Coalition: Commanded by Napoleon, Franco-German forces defeated a reinforced Austrian corps at the Battle of Abensberg.
 * 1828 – French explorer René Caillié reached Timbuktu in present-day Mali, and later received a 9,000-franc prize from the Société de Géographie for being the first European to return with a description of the city.
 * 1914 – A fire and a gun battle between the Colorado National Guard and striking coal miners led to 17 deaths in the Ludlow Massacre.
 * 1939 – Adolf Hitler's 50th birthday was celebrated as a national holiday in Nazi Germany.
 * 1939 – Billie Holiday recorded the song "Strange Fruit", which later became an emblem of the civil rights movement.
 * 1968 – Pierre Trudeau was sworn in as prime minister of Canada, succeeding Lester B. Pearson.
 * 1968 – Enoch Powell (pictured), a British Conservative member of Parliament, made a controversial speech in opposition to immigration and anti-discrimination legislation, resulting in his removal from the shadow cabinet.
 * 1978 – Korean Air Lines Flight 902 was shot down after violating Soviet airspace and was forced to make an emergency landing.
 * 1999 – Students Eric Harris and Dylan Klebold carried out a massacre at Columbine High School, killing 13 people before committing suicide.
 * 2004 – An incomplete tunnel leading to Singapore's Nicoll Highway MRT station collapsed that led to four deaths and the station's relocation.
 * 2008 – American racing driver Danica Patrick won the Indy Japan 300, becoming the first woman to win an IndyCar auto race.
 * 2008 – Fernando Lugo became the first candidate not from the Colorado Party candidate to be elected President of Paraguay in 61 years.
 * Born/died this day: | Cædwalla of Wessex |d|689| Elizabeth Barton|d|1534| William Bedloe|b|1650| David Brainerd|b|1718| John Abernethy|d|1831| Paul Poiret|b|1879| Dave Bancroft|b|1891| Frances Ames|b|1920| Elmer Gedeon|d|1944| Vjekoslav Luburić|d|1969| Nina Davuluri|b|1989| Kojo Laing|d|2017

April 20: First day of Ridván (Baháʼí Faith, 2024); 420 (cannabis culture)

 * 1535 – Sun dogs were observed over Stockholm, Sweden, inspiring the painting Vädersolstavlan (depicted), the oldest coloured depiction of the city.
 * 1818 – Four days after the Court of King's Bench upheld an English murder suspect's right to a trial by battle in Ashford v Thornton, the plaintiff declined to fight, allowing the defendant to go free.
 * 1942 – World War II: German and Italian forces began a large-scale counter-insurgency operation in occupied Yugoslavia.
 * 1968 – South African Airways Flight 228 crashed shortly after take-off from Windhoek in South West Africa, resulting in 123 deaths.
 * 2010 – An explosion on Deepwater Horizon, an offshore rig in the Gulf of Mexico, resulted in the largest marine oil spill in history.


text:
Wikipedia:Selected anniversaries/April 21

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 * 753 BC – Romulus and Remus (depicted) legendarily founded the city of Rome, according to the calculations of ancient Roman scholar Varro Reatinus.
 * 43 BC – Forces led by Mark Antony fought the Battle of Mutina against those of Decimus Brutus, one of Julius Caesar's assassins.
 * 995 - Ælfric of Abingdon was appointed Archbishop of Canterbury
 * 1509 – Henry VIII became King of England, following the death of his father Henry VII, eventually becoming a significant figure in the history of the English monarchy.
 * 1789 – The Ladies of Trenton social club hosted a reception (depicted) for President-elect George Washington as he journeyed to New York City for his first inauguration.
 * 1925 or 1926 – Al-Baqi Cemetery in Medina, the site of the mausoleum of four of the Twelve Imams of Shia Islam, was demolished by Wahhabis.
 * 1934 – The "Surgeon's Photograph", purportedly showing the Loch Ness Monster (later revealed to be a hoax), was published in the Daily Mail.
 * 1958 – United Airlines Flight 736 collided with a U.S. Air Force fighter jet over southern Nevada, resulting in the deaths of all 49 people on board both aircraft.
 * 1962 – The Century 21 Exposition, the first world's fair in the United States since World War II, opened in Seattle.
 * 1970 – In response to a dispute over wheat production quotas, Leonard Casley declared his 75 km2 farm in Western Australia to be an independent country as the Hutt River Province.
 * 2010 – Ukraine and Russia signed the Kharkiv Pact, extending the Russian lease on naval facilities in Crimea.
 * 2014 – The city of Flint, Michigan, U.S., changed its water source to the Flint River, which exposed residents to lead poisoning.
 * Born/died: | Bardas|d|866| Bajkam|d|941| Anselm of Canterbury|d|1109| Petrus Apianus|d|1552| Simon de la Loubère|b|1642| Jan Boeckhorst|d|1668| Max Weber|b|1864| Ignatius Zakka I Iwas|b|1931| Carsten Borchgrevink |d|1934| John Maynard Keynes|d|1946| Mike Wingfield|b|1954| Dorothy Eady|d|1981| Vivian Maier|d|2009

April 21

 * 900 – A debt was pardoned by the chief of Tondo on the island of Luzon and recorded on the Laguna Copperplate Inscription, the earliest known calendar-dated document found in the Philippines.
 * 1615 – The Wignacourt Aqueduct (pictured) in Malta was inaugurated and was used to carry water to Valletta for about 300 years.
 * 1836 – Forces of the Republic of Texas led by Sam Houston defeated the Mexican troops of General Antonio López de Santa Anna in the Battle of San Jacinto, the decisive and final battle of the Texas Revolution.
 * 1975 – South Vietnamese president Nguyễn Văn Thiệu resigned on hearing of the fall of Xuân Lộc, the last battle of the Vietnam War.
 * 2021 – The Indonesian Navy submarine Nanggala sank, resulting in the deaths of all 53 people on board.


text:
Banyule

Banyule may refer to places in Australia named after an Indigenous Australian word for "hill":

 * Banyule, Victoria, a locality within Heidelberg, Victoria
 * Banyule City Council, a local government area in Victoria
 * Banyule Homestead, historic property in Victoria

title: Banyule


text:
Wikipedia:Selected anniversaries/April 22

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Germaine de Staël |b|1766| James Hargreaves |d|1778| Emily Davies |b|1830| Lewis Powell|b|1844 Neal Ball |b|1881| Laura Gilpin |b|1891| Kathleen Ferrier |b|1912| Jack Nicholson |b|1937| Luang Por Dhammajayo|b|1944| Käthe Kollwitz |d|1945| Wilhelm Cauer |d|1945| Dee Duponte |d|1971| Emilio Segrè |d|1989 Donna Williams |d|2017
 * 1864 – The U.S. Congress authorized the creation of a two-cent coin (pictured), the first U.S. currency to bear the phrase "In God We Trust".
 * 1945 – About 600 prisoners of the Jasenovac concentration camp in the Independent State of Croatia revolted, but only 80 managed to escape while the remainder were killed by the Ustaše regime.
 * 1948 – Civil War in Mandatory Palestine: The Jewish paramilitary group Haganah captured Haifa from the Arab Liberation Army.
 * 1993 – Stephen Lawrence, a black British teenager, was murdered while waiting for a bus in Eltham, London, leading to cultural changes of attitudes on racism and the police, and to the law and police practice.
 * 2000 – In a pre-dawn raid, U.S. federal agents seized six-year-old Elián González from his relatives' home in Miami and returned him to his Cuban father.
 * 2004 – Flammable cargo exploded at a railway station in Ryongchon, North Korea, killing at least 54 people and injuring more than a thousand others.
 * 2013 – The Royal Canadian Mounted Police arrested two men who were plotting to commit terrorist attacks against Via Rail operations.
 * 2022 – American climate activist Wynn Bruce set himself on fire outside the United States Supreme Court Building in an apparent protest against the climate crisis.
 * Born/died: | Pope Caius |d|296| Miguel de Cervantes |d|1616| James Sullivan |b|1744|


text:
Automobiles René Bonnet

Automobiles René Bonnet was a French automobile maker.

The firm was the continuation of Deutsch et Bonnet (DB) by René Bonnet when Charles Deutsch, the "D" in DB, founded his own firm CD. The business was based at Champigny-sur-Marne to the south-east of central Paris.

History
A principal cause of the breach had involved the determination of Deutsch to stay loyal to Panhard engines while Bonnet was keen to switch to Renault power plants. The DB Le Mans, a 2+2 convertible, continued in production as the René Bonnet Le Mans, still on a front-wheel drive Panhard-based chassis albeit now equipped with Renault engines. Renault's 1,108 cc inline-four engine was also used for the Missile, a strict two-seater convertible based on the Le Mans but with a re-worked front end, and for the mid-engined Djet.

The company produced light front-wheel drive and mid-engined sports cars with very aerodynamic fiberglass bodies mainly powered by enhanced Renault engines. Its cars participated in the Le Mans 24 Hours race in 1962, 1963, and 1964. Management concentration on racing activity may nevertheless have come at the expense of commercial focus, and relatively few cars were sold during this period: by 1964 the cash was running out.

In 1962 the René Bonnet company launched its Djet model, generally remembered in retrospect as a Matra, although 198 Bonnet Djets were sold between 1962 and 1964 (179 of these were to the lowest powered "Djet I" specifications with 65 PS). A further 1,491 would be sold as Matra Djets between 1965 and 1968. The cars usually featured Renault's four-cylinder 1,108 cc engine, but some competition versions received a considerably more powerful smaller twin-cam, 996 cc unit. The earlier DB-based Missile and Le Mans were not brought back into production after the Matra takeover.

The firm worked increasingly closely with its principal investor Matra. Matra was at the time an armaments manufacturer concentrating on missiles, but they were also enthusiastic about the future of the fibreglass technology in which Bonnet was a pioneer. An important role in bringing Bonnet's business and Matra together was also contributed by an energetic former fighter pilot and national politician called André Moynet whose involvement with the enterprise appears to have outlasted Bonnet's own. Matra's rapidly evolving partnership with René Bonnet's auto-making business was the beginning of the subsequently better known Matra Automobile division, formally inaugurated in October 1964. After this Bonnet himself appears to have had little further significant involvement in the business that for two and a half years had carried his name.

Cars

 * René Bonnet Le Mans: 1962–1964
 * René Bonnet Missile: 1962–1964
 * René Bonnet Djet: 1962–1964 (and subsequently produced as Matra-Bonnet Djet/Matra Jet until 1967)
 * René Bonnet Aérojet: 1964–1965 (competition car, only nine built)

title: Automobiles René Bonnet


text:
Wikipedia:Selected anniversaries/April 23

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 * 1348 – The first knights of the Order of the Garter, an order of chivalry founded by King Edward III of England, were appointed.
 * 1467 – Albanian commander Skanderbeg entered Krujë, breaking a 10-month siege by Ottoman forces.
 * 1661 – Charles II was crowned King of England, Scotland and Ireland at Westminster Abbey.
 * 1724 – Johann Sebastian Bach leads the first performance of his cantata Du Hirte Israel, höre, BWV 104, illustrating the topic of the Good Shepherd in pastoral music.
 * 1891 – Chilean Civil War: The armored frigate Blanco Encalada was sunk at the Battle of Caldera Bay, the first ironclad warship lost to a self-propelled torpedo.
 * 1918 – First World War: The British Royal Navy launched unsuccessful raids on Ostend and Zeebrugge in German-occupied Belgium.
 * 1920 – The Grand National Assembly of Turkey, the country's unicameral legislature, first met in Ankara in the midst of the Turkish War of Independence.
 * 1927 – Cardiff City defeated Arsenal 1–0 in the FA Cup final (match programme pictured) in the only time the FA Cup has been won by a non-English team.
 * 1942 – Second World War: In retaliation for the Royal Air Force's bombing of Lübeck, the Luftwaffe began a series of air raids across England, beginning with Exeter.
 * 1951 – American journalist William N. Oatis was arrested for espionage by the communist government of Czechoslovakia.
 * 1954 – Batting for the Milwaukee Braves against Vic Raschi of the St. Louis Cardinals, Hank Aaron hit the first of his 755 home runs in Major League Baseball.
 * 1971 – The Rolling Stones released Sticky Fingers, the first album on their own label, Rolling Stones Records.
 * 2009 – The gamma-ray burst GRB 090423 was detected coming from the most distant astronomical object of any kind known at the time.
 * 2010 – Arizona governor Jan Brewer signed into law the controversial anti–illegal immigration bill SB 1070, much of which was later struck down by the U.S. Supreme Court.
 * 2019 – A landslide triggered the collapse of a jade mine in Hpakant, Myanmar, resulting in six confirmed deaths and presumed dozens more.
 * Born/died this day: | Wihtred of Kent |d|725| Béla III of Hungary |d|1196| Joan of Acre |d|1307| Karl Friedrich Bahrdt |d|1792| Jim Bottomley |b|1900| Halston |b|1932| Roy Orbison |b|1936| Kathy Lynch |b|1957| Leni Robredo|b|1965


text:
Wikipedia:Selected anniversaries/April 24

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 * 1704 – John Campbell released the first issue of The Boston News-Letter, the first continuously published newspaper in British North America.
 * 1800 – The Library of Congress (building pictured), the de facto national library of the United States, was established as part of an act of Congress providing for the transfer of the nation's capital from Philadelphia to Washington, D.C.
 * 1866 – German composer Max Bruch conducted the premiere of his first violin concerto, which later became his most famous work.
 * 1904 – Realizing that the Russification of Lithuania was not working, the Russian Empire lifted the 40-year-old ban on publications written in Lithuanian language using the Latin alphabet.
 * 1913 – The Woolworth Building in New York City officially opened; at the time, it was the tallest building in the world, with a height of 792 ft.
 * 1915 – The Armenian Genocide in the Ottoman Empire began with the arrest and deportation of hundreds of prominent Armenians in Constantinople.
 * 1918 – First World War: The Second Battle of Villers-Bretonneux began, which contained the first instance of tanks fighting against each other.
 * 1922 – The first portion of the Imperial Wireless Chain, a strategic international wireless telegraphy communications network created to link the countries of the British Empire, opened.
 * 1932 – An estimated 400 ramblers committed a wilful mass trespass of Kinder Scout (pictured) in the Peak District to highlight the denial of access to areas of open country in England.
 * 1933 – Nazi Germany began its persecution of Jehovah's Witnesses by shutting down the Watch Tower Society office in Magdeburg.
 * 1944 – World War II: The British Special Boat Service executed a successful raid to destroy an Axis radio station on the Greek island of Santorini.
 * 1965 – Cold War: The Dominican Civil War broke out due to tensions following a military coup against the democratically elected government of President Juan Bosch two years earlier.
 * 1980 – Eight U.S. servicemen died in Operation Eagle Claw, a failed attempt to rescue the captives in the Iran hostage crisis.
 * 2011 – Secret documents relating to detainees at the United States' Guantanamo Bay detention camp were released on WikiLeaks and several independent news organizations.
 * 2013 – A building in the Savar Upazila of Dhaka, Bangladesh, collapsed, killing 1,134 people, making it the deadliest accidental structural failure in modern history.
 * Born/died this day: | Xu Guangqi |b|1562| Vincent de Paul |b|1581| Axel von Fersen the Elder |d|1794| Anthony Trollope |b|1815| Robert Howard Hodgkin |b|1877| Benjamin Lee Whorf |b|1897| Mimi Smith! |b|1906| James Wood Bush |d|1906| G. Stanley Hall |d|1924| Bridget Riley |b|1931| Richard M. Daley |b|1942| Laurentia Tan |b|1979| Kelly Clarkson |b|1982| Sigrid Agren |b|1991| Sathya Sai Baba |d|2011

April 24: Armenian Genocide Remembrance Day (1915); Administrative Professionals Day in various countries (2024)

 * 1837 – A fire broke out in Surat, India, which went on to destroy about 75% of the city.
 * 1914 – The Franck–Hertz experiment, the first electrical measurement to clearly demonstrate quantum mechanics, was presented to the German Physical Society.
 * 1916 – Irish republicans led by Patrick Pearse began the Easter Rising against British rule in Ireland, and proclaimed the Irish Republic an independent state.
 * 1990 – The Hubble Space Telescope (pictured) was launched aboard STS-31 by Space Shuttle Discovery.
 * 1993 – The Provisional Irish Republican Army detonated a truck bomb in London's financial district in Bishopsgate, killing one person, injuring forty-four others, and causing damage that cost £350 million to repair.


text:
Wikipedia:Selected anniversaries/April 25

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 * 775 – The Abbasid army won a decisive victory over the forces of rebelling Armenian princes at the Battle of Bagrevand.
 * 799 – Pope Leo III was attacked by partisans of his predecessor Adrian I, but was rescued and taken to Charlemagne, as described in the epic Karolus magnus et Leo papa.
 * 1644 – Ming–Qing transition: The Ming dynasty of China fell when the Chongzhen Emperor committed suicide during a peasant rebellion led by Li Zicheng.
 * 1920 – At the San Remo conference, the principal Allies of World War I passed a resolution allocating League of Nations mandates for the administration of former Ottoman territories in the Middle East.
 * 1920 – A march by blind people from across the United Kingdom to protest at poor working conditions ended at Trafalgar Square, London.
 * 1932 – Gladys Elinor Watkins consecrated the carillon of the National War Memorial in Wellington, New Zealand (dedication pictured).
 * 1946 – Two passenger trains collided in Naperville, Illinois, leaving 45 people dead and some 125 injured.
 * 1964 – 109 individuals were arrested in a police raid on a gay bar near Chicago.
 * 1982 – British prime minister Margaret Thatcher told journalists in Downing Street to "rejoice" upon hearing news of the successful recapture of South Georgia from Argentine forces in the Falklands War.
 * 1990 – Violeta Chamorro took office as President of Nicaragua, becoming the first female head of state in the Americas to have been elected in her own right.
 * Born/died: | Géza I of Hungary |d|1077| Roger de Quincy, 2nd Earl of Winchester |d|1264| Anders Celsius |d|1744| Edward II of England |b|1284| Emer de Vattel |b|1714| Charles Sumner Tainter |b|1854| Guy Bradley |b|1870| Kojo Tovalou Houénou |b|1887| Henri Duveyrier |d|1892| Joel Brand |b|1906| Thomas A. Spragens |b|1917|  Henck Arron |b|1936| Al Pacino |b|1940| You Si-kun |b|1948| Dinesh D'Souza |b|1961| John McFall |b|1981| Stefanie Zweig |d|2014| John Havlicek |d|2019

April 25: Liberation Day in Italy (1945)

 * 1643 – First English Civil War: Despite being vastly outnumbered, a Parliamentarian force under James Chudleigh defeated a Royalist army near Okehampton, Devon, at the Battle of Sourton Down.
 * 1915 – First World War: The Australian and New Zealand Army Corps landed at Anzac Cove while British and French troops landed at Cape Helles to begin the Allied invasion of the Gallipoli peninsula in the Ottoman Empire.
 * 1960 – The U.S. Navy submarine Triton (pictured) completed the first submerged circumnavigation of the world.
 * 1983 – The first issue of The Jakarta Post was published in Indonesia.
 * 2015 – Nepal was struck by a magnitude-7.8 earthquake, killing more than 8,000 people.


text:
User:Wildlifelands~enwiki

My name is Eric van Poppel and my main contribution to wikipedia is images and sound files. Especially the latter is the big advantage of the Wikipedia Encyclopedia over a printed version. Some samples:

More images and sounds can be found on my web site http://www.wildlifelands.com

title: User:Wildlifelands~enwiki


text:
Wikipedia:Selected anniversaries/April 26

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 * 1865 – U.S. Army soldiers cornered and fatally shot John Wilkes Booth, the assassin of U.S. president Abraham Lincoln, ending a twelve-day manhunt.
 * 1941 – Boris Kidrič and Edvard Kardelj founded the Liberation Front of the Slovene Nation, the main anti-fascist Slovene civil-resistance and political organization during World War II.
 * 1944 – World War II: U.S. Navy submarines began attacks on Japan's Take Ichi convoy as it sailed in waters between Taiwan and the Philippines, eventually sinking four vessels and killing more than 4,000 troops.
 * 1958 – Service ended on the Baltimore and Ohio Railroad's Royal Blue Line, one of the first major electrified train lines in the U.S. (steam train pictured).
 * 1970 – The World Intellectual Property Organization (WIPO) came into being when the WIPO Convention entered into force.
 * 1989 – An editorial was published in the People's Daily denouncing the growing unrest in Tiananmen Square in Beijing which would remain contentious through the remainder of the protests.
 * 2007 – Controversy surrounding the relocation of the Bronze Soldier of Tallinn, a Soviet Red Army World War II memorial in Tallinn, Estonia, erupted into mass protests and riots.
 * 2012 – The International Hydrographic Organization abandoned South Korean-led 'attempts to rename the Sea of Japan.
 * Born/died: | Chen Jingxuan |d|893| Jean Fernel |d|1558|Samuel Bellamy |d|1717|  Maria Amalia of Naples and Sicily |b|1782| Nano Nagle |d|1784| Ludwig Wittgenstein |b|1889| Hack Wilson |b|1900| I. M. Pei |b|1917| Srinivasa Ramanujan |d|1920| Margaret Gowing |b|1921| Margaret Scott |b|1922Anne McLaren |b|1927| Giorgio Moroder |b|1940| Morihei Ueshiba |d|1969


text:
Wikipedia:Selected anniversaries/April 27

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 * 395 – Aelia Eudoxia married Byzantine emperor Arcadius without the knowledge or consent of Rufinus, the Praetorian prefect who had intended for his own daughter to wed the emperor.
 * 1521 – Filipino natives led by chieftain Lapulapu killed Portuguese explorer Ferdinand Magellan at the Battle of Mactan.
 * 1522 – Four Years' War: The combined forces of Spain and the Papal States defeated a French and Venetian army at the Battle of Bicocca.
 * 1777 – American Revolutionary War: British Army regulars defeated Patriot militias in the Battle of Ridgefield, galvanizing resistance in the Connecticut Colony.
 * 1810 – Ludwig van Beethoven composed his Bagatelle No. 25 in A minor, better known as "Für Elise", one of his most popular compositions.
 * 1904 – Chris Watson became the first prime minister of Australia from the Australian Labor Party.
 * 1949 – In response to the treatment of Lorenzo Gamboa under the White Australia policy, the Philippine House of Representatives passed a bill banning Australians from the country.
 * 1961 – Prime Minister Milton Margai led the Sierra Leone Colony and Protectorate to independence from the United Kingdom.
 * 1967 – The Expo 67 world's fair opened in Montreal, with 62 nations participating and more than 50 million visitors ultimately attending.
 * 1985 – The black-ball final, one of the most famous snooker matches in history, began between Steve Davis and Dennis Taylor (pictured).
 * 2012 – Unknown perpetrators carried out a series of four bombings in Dnipropetrovsk, Ukraine.
 * Born/died: | Pope Leo XI |d|1605| Mary Wollstonecraft |b|1759| Margaret Macpherson Grant |b|1834| Ralph Waldo Emerson |d|1882| Sergei Prokofiev |b|1891| Draža Mihailović |b|1893| Rogers Hornsby |b|1896| Coretta Scott King |b|1927| Russell T Davies |b|1963| Cory Booker |b|1969| Vinod Khanna |d|2017 Per Holknekt |b|1960


text:
Wikipedia:Selected anniversaries/April 28

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Rhys ap Gruffydd |d|1197| Shajar al-Durr |d|1257| James Monroe |b|1758| Tobias Asser |b|1838| Hertha Ayrton |b|1854| Antoine Samuel Adam-Salomon |d|1881| Tristan Tzara |b|1896| Josiah Willard Gibbs |d|1903| Oskar Schindler |b|1908| Hermann Fegelein |d|1945| Elena Kagan |b|1960|Penélope Cruz |b|1974| Bradley Wiggins |b|1980| David Freese |b|1983| Xiaxue|d|1984| Alf Ramsey |d|1999
 * 224 – The ancient Iranian Parthian Empire fell to the Sasanids after its forces were defeated at the Battle of Hormozdgan.
 * 1611 – The University of Santo Tomas in Manila, one of the oldest existing universities in Asia and one of the world's largest Catholic universities by enrollment, was founded.
 * 1783 – Second Anglo-Mysore War: British troops surrendered the fortress of Bednore in southwestern India to French and Mysorean forces; many of the prisoners were later murdered.
 * 1887 – A week after being arrested by the Prussian Secret Police, French police inspector Guillaume Schnaebelé (pictured) was released on the order of William I, German Emperor, defusing a possible war.
 * 1910 – Frenchman Louis Paulhan landed his biplane at Manchester (pictured), having departed from London the previous day, to win the world's first long-distance air race
 * 1941 – World War II: Presaging a campaign of genocide against the Serbs of Croatia, around 190 people were massacred by members of the Ustaše movement in Gudovac.
 * 1952 – Japan and the Republic of China signed the Treaty of Taipei, officially ending the Second Sino-Japanese War seven years after fighting ended due to World War II.
 * 1971 – Scottish trade unionist Jimmy Reid condemned the capitalist "rat race" in his inaugural address as Rector of the University of Glasgow.
 * 1973 – The album The Dark Side of the Moon by the British progressive rock band Pink Floyd entered the Billboard Top LPs & Tape chart, on which it spent a record 942 weeks.
 * 1988 – Aloha Airlines Flight 243 experienced explosive decompression while airborne between Hilo and Honolulu, Hawaii, with one fatality as a flight attendant was ejected from the aircraft.
 * 1999 – A 14-year-old former student in Taber, Alberta, opened fire at his high school, killing one student and wounding another in Canada's first fatal school shooting in more than two decades.
 * 2008 – The 1,388-foot-tall (423.2 m) Trump International Hotel and Tower in Chicago, with the world's highest residence above ground level at the time, held its grand opening.
 * Born/died this day:


text:
Wikipedia:Selected anniversaries/April 29

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 * 1386 – The Grand Duchy of Lithuania decisively won the Battle of the Vikhra River, forcibly making the Principality of Smolensk a vassal state.
 * 1760 – Seven Years' War: France began an unsuccessful attempt to retake Quebec City, which had been captured by Britain.
 * 1826 – In Parramatta, Australia, Scottish astronomer James Dunlop discovered Centaurus A (pictured), which was later recognised as one of the nearest radio galaxies to Earth.
 * 1863 – Confederate forts at Grand Gulf survived a bombardment by Union gunboats, preventing Ulysses S. Grant's troops from crossing the Mississippi River at that point.
 * 1910 – Parliament passed the People's Budget, the first budget in British history with the express intent of redistributing wealth.
 * 1945 – World War II: The U.S. Army liberated Dachau, the first Nazi concentration camp, and killed German prisoners of war.
 * 1970 – Vietnam War: South Vietnamese forces began the Cambodian campaign, aiming to attack North Vietnamese jungle bases.
 * 1975 – Vietnam War: North Vietnam concluded its East Sea Campaign by capturing all of the Spratly Islands held by South Vietnam.
 * 1991 – A powerful tropical cyclone struck Chittagong, Bangladesh, killing at least 138,000 people and leaving up to 10 million homeless across the region.
 * 1992 – The acquittal of policemen who had beaten African-American motorist Rodney King sparked six days of civil unrest in Los Angeles (damage pictured), during which 63 people were killed.
 * 1997 – The Chemical Weapons Convention entered into force, outlawing the production, stockpiling and use of chemical weapons in the 87 countries that had ratified the convention.
 * 2011 – Watched by a worldwide television audience of tens of millions, Prince William and Catherine Middleton were married at Westminster Abbey in London.
 * 2015 – The ringleaders of the Bali Nine were executed in Indonesia for attempting to smuggle 8.3 kg of heroin to Australia in 2005.
 * Born/died this day: | Catherine of Siena |d|1380| Louis II of Anjou |d|1417| Thomas Cooper |d|1594| James Butler, 2nd Duke of Ormonde |b|1665| Georgia Hopley |b|1858| Thomas Beecham |b|1879| Hendrik Nicolaas Werkman |b|1882| Harold Urey |b|1893| John Compton |b|1925| Rae Johnstone |d|1964| Uma Thurman |b|1970| Arthur B. C. Walker Jr. |d|2001


text:
Wikipedia:Selected anniversaries/April 30

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 * 1006 – SN 1006 (remnant pictured), the brightest supernova in recorded history, first appeared in the constellation Lupus.
 * 1789 – George Washington took the oath of office as the first president of the United States at Federal Hall in New York City.
 * 1803 – The United States purchased France's claim to the Louisiana Territory for 80 million francs, or less than US$.03 per acre ($.07/ha).
 * 1883 – New York governor Grover Cleveland signed legislation that led to the creation of Niagara Falls State Park, the United States' first state park.
 * 1894 – A crowd of workers, unemployed due to the Panic of 1893, concluded the first significant popular protest march on Washington D.C.
 * 1897 – British physicist J. J. Thomson and his team announce the discovery of the electron.
 * 1927 – The Federal Industrial Institute for Women opened near Alderson, West Virginia, as the first federal prison for women in the United States.
 * 1927 – Douglas Fairbanks and Mary Pickford became the first two celebrities to make imprints of their hands and feet in cement (Pickford's pictured) at Grauman's Chinese Theatre in Hollywood, California.
 * 1945 – World War II: As Allied forces closed in on Berlin, Nazi leader Adolf Hitler committed suicide in the Führerbunker with Eva Braun one day after their marriage.
 * 1982 – Sixteen monks and a nun of the Hindu organisation Ananda Marga were beaten to death and set on fire in Calcutta, India.
 * 1994 - Riverdance was performed for the first time, as the interval act for the Eurovision Song Contest.
 * 2000 – Faustina Kowalska, a Polish nun whose apparitions of Jesus inspired the Catholic devotion to the Divine Mercy, was canonized by Pope John Paul II.
 * 2004 – The New Yorker published an online article and photographs detailing accounts of torture and abuse by American military personnel of Iraqi prisoners held at Abu Ghraib prison in Baghdad.
 * 2009 – A Dutch man drove his car at high speed into a parade in an attempt to kill the Dutch royal family.
 * Born/died: | Jean-Baptiste de La Salle |b|1651| Robert Plot |d|1696| Rodrigo Anes de Sá Almeida e Meneses |d|1733| Joseph Dart |b|1799| Eugen Bleuler |b|1857| Dadasaheb Phalke |b|1870| Luigi Russolo |b|1885| Dorival Caymmi |b|1914| Roger L. Easton |b|1921| Alben W. Barkley |d|1956| Meredith L. Patterson |b|1977


text:
Bimodule

In abstract algebra, a bimodule is an abelian group that is both a left and a right module, such that the left and right multiplications are compatible. Besides appearing naturally in many parts of mathematics, bimodules play a clarifying role, in the sense that many of the relationships between left and right modules become simpler when they are expressed in terms of bimodules.

Definition
If R and S are two rings, then an R-S-bimodule is an abelian group (M, +) such that:
 * 1) M is a left R-module and a right S-module.
 * 2)  For all r in R, s in S and m in M: $$(r.m).s = r.(m.s) .$$

An R-R-bimodule is also known as an R-bimodule.

Examples

 * For positive integers n and m, the set Mn,m(R) of n × m matrices of real numbers is an R-S-bimodule, where R is the ring Mn(R) of n × n matrices, and S is the ring Mm(R) of m × m matrices. Addition and multiplication are carried out using the usual rules of matrix addition and matrix multiplication; the heights and widths of the matrices have been chosen so that multiplication is defined. Note that Mn,m(R) itself is not a ring (unless n = m), because multiplying an n × m matrix by another n × m matrix is not defined. The crucial bimodule property, that (r.x).s = r.(x.s), is the statement that multiplication of matrices is associative (which, in the case of a matrix ring, corresponds to associativity).
 * Any algebra A over a ring R has the natural structure of an R-bimodule, with left and right multiplication defined by r.a = φ(r)a and a.r = aφ(r) respectively, where φ : R → A is the canonical embedding of R into A.
 * If R is a ring, then R itself can be considered to be an R-R-bimodule by taking the left and right actions to be multiplication – the actions commute by associativity. This can be extended to Rn (the n-fold direct product of R).
 * Any two-sided ideal of a ring R is an R-R-bimodule, with the ring multiplication both as the left and as the right multiplication.
 * Any module over a commutative ring R has the natural structure of a bimodule. For example, if M is a left module, we can define multiplication on the right to be the same as multiplication on the left. (However, not all R-bimodules arise this way: other compatible right multiplications may exist.)
 * If M is a left R-module, then M is an R-Z-bimodule, where Z is the ring of integers. Similarly, right R-modules may be interpreted as Z-R-bimodules. Any abelian group may be treated as a Z-Z-bimodule.
 * If M is a right R-module, then the set EndR(M) of R-module endomorphisms is a ring with the multiplication given by composition. The endomorphism ring EndR(M) acts on M by left multiplication defined by f.x = f(x). The bimodule property, that (f.x).r = f.(x.r), restates that f is  a R-module homomorphism from M to itself. Therefore any right R-module M is an EndR(M)-R-bimodule. Similarly any left R-module N is an R-EndR(N)op-bimodule.
 * If R is a subring of S, then S is an R-R-bimodule. It is also an R-S- and an S-R-bimodule.
 * If M is an S-R-bimodule and N is an R-T-bimodule, then M ⊗R N is an S-T-bimodule.

Further notions and facts
If M and N are R-S-bimodules, then a map f : M → N is a bimodule homomorphism if it is both a homomorphism of left R-modules and of right S-modules.

An R-S-bimodule is actually the same thing as a left module over the ring R ⊗Z Sop, where Sop is the opposite ring of S (where the multiplication is defined with the arguments exchanged). Bimodule homomorphisms are the same as homomorphisms of left R ⊗Z Sop modules. Using these facts, many definitions and statements about modules can be immediately translated into definitions and statements about bimodules. For example, the category of all R-S-bimodules is abelian, and the standard isomorphism theorems are valid for bimodules. There are however some new effects in the world of bimodules, especially when it comes to the tensor product: if M is an R-S-bimodule and N is an S-T-bimodule, then the tensor product of M and N (taken over the ring S) is an R-T-bimodule in a natural fashion. This tensor product of bimodules is associative (up to a unique canonical isomorphism), and one can hence construct a category whose objects are the rings and whose morphisms are the bimodules. This is in fact a 2-category, in a canonical way – 2 morphisms between R-S-bimodules M and N are exactly bimodule homomorphisms, i.e. functions
 * $$f: M \rightarrow N$$

that satisfy for m ∈ M, r ∈ R, and s ∈ S. One immediately verifies the interchange law for bimodule homomorphisms, i.e.
 * 1) $$f(m+m') = f(m)+ f(m')$$
 * 2) $$f(r.m.s) = r.f(m).s$$,
 * $$(f'\otimes g')\circ (f\otimes g) = (f'\circ f)\otimes(g'\circ g) $$

holds whenever either (and hence the other) side of the equation is defined, and where ∘ is the usual composition of homomorphisms. In this interpretation, the category End(R) = Bimod(R, R) is exactly the monoidal category of R-R-bimodules with the usual tensor product over R the tensor product of the category. In particular, if R is a commutative ring, every left or right R-module is canonically an R-R-bimodule, which gives a monoidal embedding of the category R-Mod into Bimod(R, R). The case that R is a field K is a motivating example of a symmetric monoidal category, in which case R-Mod = K-Vect, the category of vector spaces over K, with the usual tensor product ⊗ = ⊗K giving the monoidal structure, and with unit K. We also see that a monoid in Bimod(R, R) is exactly an R-algebra. Furthermore, if M is an R-S-bimodule and L is an T-S-bimodule, then the set HomS(M, L) of all S-module homomorphisms from M to L becomes a T-R-bimodule in a natural fashion. These statements extend to the derived functors Ext and Tor.

Profunctors can be seen as a categorical generalization of bimodules.

Note that bimodules are not at all related to bialgebras.

title: Bimodule


text:
Flat module

In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion free modules. Formally, a module M over a ring R is flat if taking the tensor product over R with M preserves exact sequences. A module is faithfully flat if taking the tensor product with a sequence produces an exact sequence if and only if the original sequence is exact.

Flatness was introduced by in his paper Géometrie Algébrique et Géométrie Analytique.

Definition
A left module $M$ over a ring $R$ is flat if the following condition is satisfied: for every injective linear map $$\varphi: K \to L$$ of right $R$-modules, the map
 * $$\varphi \otimes_R M: K \otimes_R M \to L \otimes_R M$$

is also injective, where $$\varphi \otimes_R M$$ is the map induced by $$k \otimes m \mapsto \varphi(k) \otimes m.$$

For this definition, it is enough to restrict the injections $$\varphi$$ to the inclusions of finitely generated ideals into $R$.

Equivalently, an $R$-module $M$ is flat if the tensor product with $M$ is an exact functor; that is if, for every short exact sequence of $R$-modules $$0\rightarrow K\rightarrow L\rightarrow J\rightarrow 0,$$ the sequence $$0\rightarrow K\otimes_R M\rightarrow L\otimes_R M\rightarrow J\otimes_R M\rightarrow 0$$ is also exact. (This is an equivalent definition since the tensor product is a right exact functor.)

These definitions apply also if $R$ is a non-commutative ring, and $M$ is a left $R$-module; in this case, $K$, $L$ and $J$ must be right $R$-modules, and the tensor products are not $R$-modules in general, but only abelian groups.

Characterizations
Flatness can also be characterized by the following equational condition, which means that $R$-linear relations in $M$ stem from linear relations in $R$.

A left $R$-module $M$ is flat if and only if, for every linear relation
 * $\sum_{i=1}^m r_i x_i = 0$

with $$ r_i \in R$$ and $$x_i \in M$$, there exist elements $$y_j\in M$$ and $$a_{i,j}\in R,$$ such that
 * $\sum_{i=1}^m r_ia_{i,j}=0\qquad$ for $$j=1, \ldots, n ,$$

and
 * $x_i=\sum_{j=1}^n a_{i,j} y_j\qquad$ for $$i=1, \ldots, m.$$

It is equivalent to define $n$ elements of a module, and a linear map from $$R^n$$ to this module, which maps the standard basis of $$R^n$$ to the $n$ elements. This allows rewriting the previous characterization in terms of homomorphisms, as follows.

An $R$-module $M$ is flat if and only if the following condition holds: for every map $$f : F \to M,$$ where $$F$$ is a finitely generated free $R$-module, and for every finitely generated $R$-submodule $$K$$ of $$\ker f,$$ the map $$f$$ factors through a map $g$ to a free $R$-module $$G$$ such that $$g(K)=0:$$

Relations to other module properties
Flatness is related to various other module properties, such as being free, projective, or torsion-free. In particular, every flat module is torsion-free, every projective module is flat, and every free module is projective.

There are finitely generated modules that are flat and not projective. However, finitely generated flat modules are all projective over the rings that are most commonly considered. Moreover, a finitely generated module is flat if and only it is locally free, meaning all the localizations at prime ideals are free modules.

This is partly summarized in the following graphic.

Torsion-free modules
Every flat module is torsion-free. This results from the above characterization in terms of relations by taking $m = 1$.

The converse holds over the integers, and more generally over principal ideal domains and Dedekind rings.

An integral domain over which every torsion-free module is flat is called a Prüfer domain.

Free and projective modules
A module $M$ is projective if and only if there is a free module $G$ and two linear maps $$i:M\to G$$ and $$p:G\to M$$ such that $$p\circ i = \mathrm{id}_M.$$ In particular, every free module is projective (take $$G=M$$ and $i=p=\mathrm{id}_M$).

Every projective module is flat. This can be proven from the above characterizations of flatness and projectivity in terms of linear maps by taking $$g=i\circ f$$ and $$h=p.$$

Conversely, finitely generated flat modules are projective under mild conditions that are generally satisfied in commutative algebra and algebraic geometry. This makes the concept of flatness useful mainly for modules that are not finitely generated.

A finitely presented module (that is the quotient of a finitely generated free module by a finitely generated submodule) that is flat is always projective. This can be proven by taking $f$ surjective and $$K=\ker f$$ in the above characterization of flatness in terms of linear maps. The condition $$g(K)=0$$ implies the existence of a linear map $$i:M\to G$$ such that $$i\circ f = g,$$ and thus $$h\circ i \circ f =h\circ g = f. $$ As $f$ is surjective, one has thus $$h\circ i=\mathrm{id}_M,$$ and $M$ is projective.

Over a Noetherian ring, every finitely generated flat module is projective, since every finitely generated module is finitely presented. The same result is true over an integral domain, even if it is not Noetherian.

On a local ring every finitely generated flat module is free.

A finitely generated flat module that is not projective can be built as follows. Let $$R=F^\mathbb N$$ be the set of the infinite sequences whose terms belong to a fixed field $F$. It is a commutative ring with addition and multiplication defined componentwise. This ring is absolutely flat (that is, every module is flat). The module $$R/I,$$ where $I$ is the ideal of the sequences with a finite number of nonzero terms, is thus flat and finitely generated (only one generator), but it is not projective.

Non-examples

 * If $I$ is an ideal in a Noetherian commutative ring $R$, then $$R/I$$ is not a flat module, except if $I$ is generated by an idempotent (that is an element equal to its square). In particular, if $R$ is an integral domain, $$R/I$$ is flat only if $$I$$ equals $R$ or is the zero ideal.
 * Over an integral domain, a flat module is torsion free. Thus a module that contains nonzero torsion elements is not flat. In particular $$\Q/\Z$$ and all fields of positive characteristics are non-flat $$\Z$$-modules, where $$\Z$$ is the ring of integers, and $$\Q$$ is the field of the rational numbers.

Direct sums, limits and products
A direct sum $$\textstyle\bigoplus_{i \in I} M_i$$ of modules is flat if and only if each $$M_i$$ is flat.

A direct limit of flat is flat. In particular, a direct limit of free modules is flat. Conversely, every flat module can be written as a direct limit of finitely-generated free modules.

Direct products of flat modules need not in general be flat. In fact, given a ring $R$, every direct product of flat $R$-modules is flat if and only if $R$ is a coherent ring (that is, every finitely generated ideal is finitely presented).

Flat ring extensions
A ring homomorphism $$R \to S$$ is flat if $S$ is a flat $R$-module for the module structure induced by the homomorphism. For example, the polynomial ring $R[t]$ is flat over $R$, for any ring $R$.

For any multiplicative subset $$S$$ of a commutative ring $$R$$, the localization $$S^{-1}R$$ is a flat $R$-algebra (it is projective only in exceptional cases). For example, $$\Q$$ is flat and not projective over $$\Z.$$

If $$I$$ is an ideal of a Noetherian commutative ring $$R,$$ the completion $$\widehat{R}$$ of $$R$$ with respect to $$I$$ is flat. It is faithfully flat if and only if $$I$$ is contained in the Jacobson radical of $$A.$$ (See also Zariski ring.)

Local property
In this section, $R$ denotes a commutative ring. If $$\mathfrak p$$ is a prime ideal of $R$, the localization at $$\mathfrak p$$ is, as usual, denoted with $$\mathfrak p$$ as an index. That is, $$R_{\mathfrak p} = (R\setminus \mathfrak p)^{-1}R,$$ and, if $M$ is an $R$-module, $$M_{\mathfrak p} = (R\setminus \mathfrak p)^{-1}M = R_{\mathfrak p}\otimes_R M.$$

If $M$ is an $R$-module the three following conditions are equivalent:
 * $$M$$ is a flat $$R$$-module;
 * $$M_\mathfrak p$$ is a flat $$R_\mathfrak p$$-module for every prime ideal $$\mathfrak p;$$
 * $$M_\mathfrak m$$ is a flat $$R_\mathfrak m$$-module for every maximal ideal $$\mathfrak m.$$

This property is fundamental in commutative algebra and algebraic geometry, since it reduces the study of flatness to the case of local rings. They are often expressed by saying that flatness is a local property.

Flat morphisms of schemes
The definition of a flat morphism of schemes results immediately from the local property of flatness.

A morphism $$f: X \to Y$$ of schemes is a flat morphism if the induced map on local rings
 * $$\mathcal O_{Y, f(x)} \to \mathcal O_{X,x}$$

is a flat ring homomorphism for any point $x$ in $X$.

Thus, properties of flat (or faithfully flat) ring homomorphisms extends naturally to geometric properties of flat morphisms in algebraic geometry. For example, consider the flat $$\mathbb{C}[t]$$-algebra $$R = \mathbb{C}[t,x,y]/(xy-t)$$ (see below). The inclusion $$\mathbb{C}[t] \hookrightarrow R$$ induces the flat morphism
 * $$\pi : \operatorname{Spec}(R) \to \operatorname{Spec}(\mathbb C[t]).$$

Each (geometric) fiber $$\pi^{-1}(t)$$ is the curve of equation $$xy = t.$$ (See also flat degeneration and deformation to normal cone.)

Let $$S = R[x_1, \dots, x_r]$$ be a polynomial ring over a commutative Noetherian ring $$R$$ and $$f \in S$$ a nonzerodivisor. Then $$S/fS$$ is flat over $$R$$ if and only if $$f$$ is primitive (the coefficients generate the unit ideal). An example is $$\mathbb{C}[t,x,y]/(xy-t),$$ which is flat (and even free) over $$\mathbb{C}[t]$$ (see also below for the geometric meaning). Such flat extensions can be used to yield examples of flat modules that are not free and do not result from a localization.

Faithful flatness
A module is faithfully flat if taking the tensor product with a sequence produces an exact sequence if and only if the original sequence is exact. Although the concept is defined for modules over a non-necessary commutative ring, it is used mainly for commutative algebras. So, this is the only case that is considered here, even if some results can be generalized to the case of modules over a non-commutaive ring.

In this section, $$f\colon R \to S$$ is a ring homomorphism of commutative rings, which gives to $$S$$ the structures of an $$R$$-algebra and an $$R$$-module. If $$S$$ is a $$R$$-module flat (or faithfully flat), one says commonly that $$S$$ is flat (or faithfully flat) over $$R, $$ and that $$f$$ is flat (or faithfully flat).

If $$S$$ is flat over $$R,$$ the following conditions are equivalent.
 * $$S$$ is faithfully flat.
 * For each maximal ideal $$\mathfrak{m}$$ of $$R$$, one has $$\mathfrak{m}S \ne S.$$
 * If $$M$$ is a nonzero $$R$$-module, then $$M \otimes_R S \ne 0.$$
 * For every prime ideal $$\mathfrak{p}$$ of $$R,$$ there is a prime ideal $$\mathfrak{P}$$ of $$S$$ such that $$\mathfrak{p} = f^{-1}(\mathfrak P).$$ In other words, the map $$f^*\colon \operatorname{Spec}(S) \to \operatorname{Spec}(R)$$ induced by $$f$$ on the spectra is surjective.
 * $$f,$$ is injective, and $$R$$ is a pure subring of $$S;$$ that is, $$M \to M \otimes_R S$$ is injective for every $$R$$-module $$M$$.

The second condition implies that a flat local homomorphism of local rings is faithfully flat. It follows from the last condition that $$I = I S \cap R$$ for every ideal $$I$$ of $$R$$ (take $$M = R/I$$). In particular, if $$S$$ is a Noetherian ring, then $$R$$ is also Noetherian.

The last but one condition can be stated in the following strengthened form: $$\operatorname{Spec}(S) \to \operatorname{Spec}(R)$$ is submersive, which means that the Zariski topology of $$\operatorname{Spec}(R)$$ is the quotient topology of that of $$\operatorname{Spec}(S)$$ (this is a special case of the fact that a faithfully flat quasi-compact morphism of schemes has this property.). See also .

Examples

 * A ring homomorphism $$R\to S$$ such that $$S$$ is a nonzero free $R$-module is faithfully flat. For example:
 * Every field extension is faithfully flat. This property is implicitly behind the use of complexification for proving results on real vector spaces.
 * A polynomial ring is a faithfully flat extension of its ring of coefficients.
 * If $$p\in R[x]$$ is a monic polynomial, the inclusion $$R \hookrightarrow R[t]/\langle p \rangle$$ is faithfully flat.
 * Let $$t_1, \ldots, t_k\in R.$$ The direct product $$\textstyle\prod_i R[t_i^{-1}]$$ of the localizations at the $$t_i$$ is faithfully flat over $$R$$ if and only if $$t_1, \ldots, t_k$$ generate the unit ideal of $$R$$ (that is, if $$1$$ is a linear combination of the $$t_i$$).
 * The direct sum of the localizations $$R_\mathfrak p$$ of $$R$$ at all its prime ideals is a faithfully flat module that is not an algebra, except if there are finitely many prime ideals.

The two last examples are implicitly behind the wide use of localization in commutative algebra and algebraic geometry.

$$0 \to A \overset{f}\to B \overset{\delta^0}\to B \otimes_A B \overset{\delta^1}\to B \otimes_A B \otimes_A B \to \cdots$$ where the coboundary operators $$\delta^n$$ are the alternating sums of the maps obtained by inserting 1 in each spot; e.g., $$\delta^0(b) = b \otimes 1-1 \otimes b$$. Then (Grothendieck) this complex is exact if $$f$$ is faithfully flat.
 * For a given ring homomorphism $$f: A \to B,$$ there is an associated complex called the Amitsur complex:

Faithfully flat local homomorphisms
Here is one characterization of a faithfully flat homomorphism for a not-necessarily-flat homomorphism. Given an injective local homomorphism $$(R, \mathfrak m) \hookrightarrow (S, \mathfrak n)$$ such that $$\mathfrak{m} S$$ is an $$\mathfrak{n}$$-primary ideal, the homomorphism $$S \to B$$ is faithfully flat if and only if the theorem of transition holds for it; that is, for each $$\mathfrak m$$-primary ideal $$\mathfrak q$$ of $$R$$, $$\operatorname{length}_S (S/ \mathfrak q S) = \operatorname{length}_S (S/ \mathfrak{m} S) \operatorname{length}_R(R/\mathfrak q).$$

Homological characterization using Tor functors
Flatness may also be expressed using the Tor functors, the left derived functors of the tensor product. A left $$R$$-module $$M$$ is flat if and only if
 * $$\operatorname{Tor}_n^R (X, M) = 0$$ for all $$n \ge 1$$ and all right $$R$$-modules $$X$$).

In fact, it is enough to check that the first Tor term vanishes, i.e., M is flat if and only if
 * $$\operatorname{Tor}_1^R (N, M) = 0$$

for any $$R$$-module $$N$$ or, even more restrictively, when $$N=R/I$$ and $$I\subset R$$ is any finitely generated ideal.

Using the Tor functor's long exact sequences, one can then easily prove facts about a short exact sequence
 * $$0 \to A \overset{f}{\longrightarrow} B \overset{g}{\longrightarrow} C \to 0$$

If $$A$$ and $$C$$ are flat, then so is $$B$$. Also, if $$B$$ and $$C$$ are flat, then so is $$A$$. If $$A$$ and $$B$$ are flat, $$C$$ need not be flat in general. However, if $$A$$ is pure in $$B$$ and $$B$$ is flat, then $$A$$ and $$C$$ are flat.

Flat resolutions
A flat resolution of a module $$M$$ is a resolution of the form
 * $$\cdots \to F_2 \to F_1 \to F_0 \to M \to 0,$$

where the $$F_i$$ are all flat modules. Any free or projective resolution is necessarily a flat resolution. Flat resolutions can be used to compute the Tor functor.

The length of a finite flat resolution is the first subscript n such that $$F_n$$ is nonzero and $$F_i=0$$ for $$i>n$$. If a module $$M$$ admits a finite flat resolution, the minimal length among all finite flat resolutions of $$M$$ is called its flat dimension and denoted $$\operatorname{fd}(M)$$. If $$M$$ does not admit a finite flat resolution, then by convention the flat dimension is said to be infinite. As an example, consider a module $$M$$ such that $$\operatorname{fd}(M)=0$$. In this situation, the exactness of the sequence $$0 \to F_0 \to M \to 0$$ indicates that the arrow in the center is an isomorphism, and hence $$M$$ itself is flat.

In some areas of module theory, a flat resolution must satisfy the additional requirement that each map is a flat pre-cover of the kernel of the map to the right. For projective resolutions, this condition is almost invisible: a projective pre-cover is simply an epimorphism from a projective module. These ideas are inspired from Auslander's work in approximations. These ideas are also familiar from the more common notion of minimal projective resolutions, where each map is required to be a projective cover of the kernel of the map to the right. However, projective covers need not exist in general, so minimal projective resolutions are only of limited use over rings like the integers.

Flat covers
While projective covers for modules do not always exist, it was speculated that for general rings, every module would have a flat cover, that is, every module M would be the epimorphic image of a flat module F such that every map from a flat module onto M factors through F, and any endomorphism of F over M is an automorphism. This flat cover conjecture was explicitly first stated in. The conjecture turned out to be true, resolved positively and proved simultaneously by L. Bican, R. El Bashir and E. Enochs. This was preceded by important contributions by P. Eklof, J. Trlifaj and J. Xu.

Since flat covers exist for all modules over all rings, minimal flat resolutions can take the place of minimal projective resolutions in many circumstances. The measurement of the departure of flat resolutions from projective resolutions is called relative homological algebra, and is covered in classics such as and in more recent works focussing on flat resolutions such as.

In constructive mathematics
Flat modules have increased importance in constructive mathematics, where projective modules are less useful. For example, that all free modules are projective is equivalent to the full axiom of choice, so theorems about projective modules, even if proved constructively, do not necessarily apply to free modules. In contrast, no choice is needed to prove that free modules are flat, so theorems about flat modules can still apply.

title: Flat module


text:
Wikipedia talk:Selected anniversaries/March 10

Three links are individually bolded, none of the articles contain more info on the event. Maybe dot-com should be bolded instead? Or, better, the Nasdaq article updated.. — Sverdrup (talk) 10:03, 28 Feb 2004 (UTC)

 * I just copied the text over. Everything will be fixed by the time this page goes live on the Main Page. --mav 15:14, 28 Feb 2004 (UTC)

 * Fixed. --mav

Should this say that Bell made his first successful phone call? Gray certainly had transmitter reciever pairs, there's Meucci's claim, etc etc. The term the seems a little strong. Rick Boatright 17:55, 8 Mar 2004 (UTC)

 * His it is. --mav

I suggest: Romans defeat Carthage in the First Punic War. Muriel 11:41, 11 Mar 2004 (UTC)

 * See Selected_anniversaries --mav 07:25, 12 Mar 2004 (UTC)

Hitler armies invasion of the rest of Czechoslovakia
I suggest:
 * 1939 - Hitler ordered German armies to enter Prague. Sparking of World War II.

info: By some historicians, this is the begining of World War II (it was the first invasion of German armies) I used the text "to enter Prague" because after the Munich Agreement - Czechoslovakia had to give its essential territory to surrounding countries -so it was not yet "invasion of Czechoslovakia" - but just its rest. —The preceding unsigned comment was added by 62.24.84.55 (talk • contribs) 15:09, 2006 January 19.

 * I think this happened on March 15 instead. -- PFHLai 17:22, 1 March 2006 (UTC)

 * Oh my mistake - you´re right! Could it be added there? For example instead of test match of cricket? —The preceding unsigned comment was added by Szalas (talk • contribs) 17:45, 2006 March 1 (UTC).
 * Thanks for the suggestion, I did that already. But it didn't bump off the cricket item.  Wikipedia has many good cricket-related pages, but we rarely get the chance to feature any of them. I almost take off the Rolls Royce bit but it stayed for the 100th anniversary.... -- PFHLai 02:00, 2 March 2006 (UTC)

Courrières mine disaster
This is of course a blatant plug for the page I am writing at the moment :) but this was Europe's biggest mining disaster by a long way (1099 dead), and it's the centenary this year. Big news in France this week... Physchim62 (talk) 12:34, 6 March 2006 (UTC)
 * You don't want this on DYK ? (We shouldn't feature the same page on both.) -- PFHLai 19:49, 6 March 2006 (UTC)
 * Posted. Hope you won't miss the DYK medal. --PFHLai 18:15, 8 March 2006 (UTC)

Painting
The painting of King Louis-Philippe is available in Commons as commons:Image:Louis-Philippe de Bourbon.jpg. -Samulili 15:58, 3 July 2006 (UTC)
 * Thanks. It's now fixed. --PFHLai 03:54, 4 July 2006 (UTC)

2012 notes
— howcheng  {chat} 07:28, 9 March 2012 (UTC)
 * Moved to Ineligible: Personal rule of Charles I, 1629-1640 (maintenance; blurb previously featured Charles I of England, which is already on January 30)
 * New articles (unused): Eliot Spitzer prostitution scandal
 * Omitted: Royal Netherlands East Indies Army, Fulgencio Batista, Thomas Playford IV, Nguyen Chanh Thi
 * Included: Invention of the telephone (2nd appearance, last in 2010; rescued from Ineligible), Battle of Ban Me Thuot (first appearance), Rings of Uranus (3rd appearance, last in 2010), Tung Chee Hwa (first appearance)
 * Repeats: Susenyos of Ethiopia (2nd consecutive appearance, 2 total)
 * Addendum: Eliot Spitzer prostitution scandal added later for balance (first appearance)

2013 notes
— howcheng  {chat} 06:34, 9 March 2013 (UTC)
 * Omitted: Susenyos I; Battle of Ban Me Thuot; Rings of Uranus; Tung Chee Hwa; Eliot Spitzer prostitution scandal
 * Included: Royal Netherlands East Indies Army (2nd appearance, last in 2011}; 1959 Tibetan uprising (3rd appearance, last in 2010); Battle of Lima Site 85 (first appearance); Mars Reconnaissance Orbiter (2nd appearance, last in 2011)
 * Repeats: Invention of the telephone (2nd consecutive appearance, 3 total)

2014 notes
— howcheng  {chat} 06:00, 9 March 2014 (UTC)
 * Omitted: Invention of the telephone; 1959 Tibetan uprising; Battle of Lima Site 85; Mars Reconnaissance Orbiter
 * Included: Susenyos I (4th appearance, last in 2012); Fulgencio Batista (7th appearance, last in 2011); Battle of Ban Me Thuot (first appearance); Tung Chee Hwa (2nd appearance, last in 2012)
 * Repeats: Royal Netherlands East Indies Army (2nd consecutive appearance, 3 total)

2015 notes
— howcheng  {chat} 08:51, 8 March 2015 (UTC)
 * Omitted: Susenyos I; Fulgencio Batista
 * Included: Invention of the telephone (4th appearance, last in 2013); Thomas Playford IV (2nd appearance, last in 2011; 50th anniversary)
 * Repeats: Royal Netherlands East Indies Army (3rd consecutive appearance, 4 total); Battle of Ban Me Thuot (2nd consecutive appearance, 4 total; 40th anniversary); Tung Chee-hwa (2nd consecutive appearance, 3 total; 10th anniversary)

2016 notes
— howcheng  {chat} 09:11, 8 March 2016 (UTC)
 * Omitted: Royal Netherlands East Indies Army; Thomas Playford IV; Battle of Ban Me Thuot; Tung Chee-hwa
 * Included: Susenyos I (5th appearance, last in 2014); 1959 Tibetan uprising (4th appearance, last in 2013); Nguyễn Chánh Thi (first appearance; 50th anniversary); Mars Reconnaissance Orbiter (3rd appearance, last in 2013)
 * Repeats: Invention of the telephone (2nd consecutive appearance, 5 total)

2017 notes
— howcheng  {chat} 08:29, 10 March 2017 (UTC)
 * Omitted: Susenyos I (ineligible—maintenance); Royal Netherlands East Indies Army (ineligible—maintenance); 1959 Tibetan uprising; Nguyễn Chánh Thi; Mars Reconnaissance Orbiter
 * Included: Battle of Neuve Chapelle (first appearance); Fulgencio Batista (8th appearance, last in 2014); Rings of Uranus (4th appearance, last in 2012; 40th anniversary); Tung Chee-hwa (4th appearance, last in 2015); Agnes Blannbekin (first appearance); Lillian Wald (first appearance); Muhammad Sayyid Tantawy (first appearance)
 * Repeats: Invention of the telephone (3rd consecutive appearance, 6 total)

2018 notes
— howcheng  {chat} 17:51, 10 March 2018 (UTC)
 * Moved to Ineligible: 1959 Tibetan uprising (maintenance)
 * Omitted: Invention of the telephone (ineligible—maintenance); Battle of Neuve Chapelle; Rings of Uranus; Tung Chee-hwa; Agnes Blannbekin; Lillian Wald; Muhammad Sayyid Tantawy
 * Included: McMahon–Hussein Correspondence (first appearance); Battle of Lima Site 85 (2nd appearance, last in 2013; 50th anniversary); Dot-com bubble (4th appearance, last in 2008; rescued from Ineligible); Eliot Spitzer prostitution scandal (2nd appearance, last in 2012; 10th anniversary); Amy Spain (first appearance); Marie-Eugénie de Jésus (first appearance); Emily Osment (first appearance)
 * Repeats: Fulgencio Batista (2nd consecutive appearance, 9 total)

2019 notes
— howcheng  {chat} 16:11, 11 March 2019 (UTC)
 * Moved to Ineligible: Tung Chee-hwa (maintenance)
 * New articles (unused): Bombing of Tokyo (10 March 1945)
 * Omitted: McMahon–Hussein Correspondence; Fulgencio Batista; Battle of Lima Site 85; Dot-com bubble; Eliot Spitzer prostitution scandal; Amy Spain; Marie-Eugénie de Jésus (ineligible—maintenance); Emily Osment (ineligible—maintenance)
 * Included: Battle of Neuve Chapelle (2nd appearance, last in 2017); Mildred Gillars (first appearance; 70th anniversary); Thomas Playford IV (3rd appearance, last in 2015); Pink Floyd (first appearance); Battle of Ban Me Thuot (4th appearance, last in 2015); Mars Reconnaissance Orbiter (4th appearance, last in 2016); John Benbow (first appearance); Charles Frederick Worth (first appearance); Muhammad Sayyid Tantawy (2nd appearance, last in 2017)

2020 notes
— howcheng  {chat} 15:57, 11 March 2020 (UTC)
 * Moved to Ineligible: Bombing of Tokyo (10 March 1945) (TFA for 2020); Dot-com bubble (maintenance)
 * New articles (ineligible): Ethiopian Airlines Flight 302 (maintenance)
 * Rescued from Ineligible (unused): Marie-Eugénie de Jésus
 * Omitted: Battle of Neuve Chapelle; Mildred Gillars; Thomas Playford IV; Battle of Ban Me Thuot; Mars Reconnaissance Orbiter; John Benbow; Charles Frederick Worth
 * Included: Battle of the Aegates (8th appearance, last in 2010; rescued from Ineligible); McMahon–Hussein Correspondence (2nd appearance, last in 2018); 1959 Tibetan uprising (5th appearance, last in 2016; rescued from Ineligible); Rings of Uranus (5th appearance, last in 2017); Tvrtko I of Bosnia (first appearance); Violet Brown (first appearance)
 * Repeats: Pink Floyd (2nd consecutive appearance, 2 total); Muhammad Sayyid Tantawy (2nd consecutive appearance, 3 total; 10th anniversary)

2021 notes
— howcheng  {chat} 07:49, 12 March 2021 (UTC)
 * New articles (ineligible): Janet Mock (maintenance)
 * Omitted: Battle of the Aegates (ineligible—TFA for 2021); McMahon–Hussein Correspondence; 1959 Tibetan uprising; Pink Floyd; Rings of Uranus; Violet Brown; Muhammad Sayyid Tantawy
 * Included: Battle of Neuve Chapelle (3rd appearance, last in 2019); Bombing of Tokyo (10 March 1945) (first appearance; rescued from Ineligible); Prosper Avril (first appearance); Mars Reconnaissance Orbiter (5th appearance, last in 2019); Marie-Eugénie de Jésus (2nd appearance, last in 2018); Nikita Parris (first appearance)
 * Repeats: Tvrtko I of Bosnia (2nd consecutive appearance, 2 total)

2022 notes
— howcheng  {chat} 21:08, 11 March 2022 (UTC)
 * Moved to Ineligible: Fulgencio Batista/1952 Cuban coup d'état (both: maintenance)
 * Omitted: Battle of Neuve Chapelle; Bombing of Tokyo (10 March 1945); 1959 Tibetan uprising; Prosper Avril; Mars Reconnaissance Orbiter; Tvrtko I of Bosnia; Marie-Eugénie de Jésus; Nikita Parris
 * Included: Battle of the Aegates (9th appearance, last in 2020; rescued from Ineligible); McMahon–Hussein Correspondence (3rd appearance, last in 2020); Mildred Gillars (2nd appearance, last in 2019); Pink Floyd (3rd appearance, last in 2020); Ethiopian Airlines Flight 302 (first appearance; rescued from Ineligible); Agnes Blannbekin (2nd appearance, last in 2017); François Girardon (first appearance); Anita Brookner (first appearance)


text:
Wikipedia:Selected anniversaries/May 1

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Eligible

 * 880 – The Nea Ekklesia church in Constantinople, on which many later cross-in-square Orthodox churches were based, was consecrated.
 * 1576 – Stephen Báthory and Anna Jagiellon were crowned as the elected rulers of the Polish–Lithuanian Commonwealth.
 * 1625 – Dutch–Portuguese War: Portuguese and Spanish forces recaptured the Brazilian city of Bahia, which had previously been captured by the Dutch Republic.
 * 1707 – Under the terms of the Acts of Union, the Kingdoms of England and Scotland merged to form the Kingdom of Great Britain, with a single parliament and government based in Westminster.
 * 1776 – The secret society known as the Order of Illuminati was founded by Adam Weishaupt and Adolph Freiherr Knigge in Ingolstadt, Bavaria, Germany.
 * 1786 – The Marriage of Figaro (audio featured), an opera buffa by Wolfgang Amadeus Mozart, premiered at the Burgtheater in Vienna.
 * 1884 – Moses Fleetwood Walker (pictured), the last African American in Major League Baseball until Jackie Robinson, played his first game for the Toledo Blue Stockings.
 * 1885 – The original Chicago Board of Trade Building opened for business.
 * 1900 – A dust explosion at a coal mine near Scofield, Utah, U.S., killed at least 200 miners.
 * 1941 – Citizen Kane, a widely acclaimed film by actor and director Orson Welles, premiered.
 * 1945 – Second World War: British and Indian forces conducted a successful airborne assault on a Japanese artillery battery during the advance to liberate Rangoon, Burma.
 * 1947 – Sicilian separatist Salvatore Giuliano and his gang fired into a crowd of May Day marchers near Piana degli Albanesi, Sicily, killing 11 and wounding 33.
 * 1950 – Gwendolyn Brooks became the first African American to receive the Pulitzer Prize for Poetry.
 * 1991 – In Major League Baseball, Rickey Henderson broke the record for stolen bases on the same night that Nolan Ryan broke his own record for no-hitters.
 * 2016 – The evacuation of nearly 88,000 people began when a wildfire swept through Fort McMurray, Alberta, Canada, and burned for another 14 months, becoming the costliest disaster in Canadian history.

 * Born/died this day: | Paul I Šubić of Bribir |d|1312| Franciscus Junius the Elder |b|1545| François de Troy |d|1730| Arthur Wellesley, 1st Duke of Wellington |b|1769| Honora Sneyd |d|1780| Adelsteen Normann |b|1848| Marie-Aimée Roger-Miclos |b|1860| Ralph Stackpole |b|1885| Henry DeWolf Smyth |b|1898| Ulric Cross |b|1917| Magda Goebbels |d|1945| Ranasinghe Premadasa |d|1993| Aram Khachaturian |d|1978

title: Wikipedia:Selected anniversaries/May 1