36 – Forces of Emperor Guangwu of the Eastern Han, under the command of Wu Han, conquer the separatist Chengjia empire, reuniting China.
274 – A temple to Sol Invictus is dedicated in Rome by Emperor Aurelian.
333 – Roman Emperor Constantine the Great elevates his youngest son Constans to the rank of Caesar.
336 – First documentary sign of Christmas celebration in Rome.
350 – Vetranio meets Constantius II at Naissus (Serbia) and is forced to abdicate his imperial title. Constantius allows him to live as a private citizen on a state pension.
508 – Clovis I, king of the Franks, is baptized into the Catholic faith at Reims, by Saint Remigius.
597 – Augustine of Canterbury and his fellow-labourers baptise in Kent more than 10,000 Anglo-Saxons.
800 – The coronation of Charlemagne as Holy Roman Emperor, in Rome.
820 – Eastern Emperor Leo V is murdered in a church of the Great Palace of Constantinople by followers of Michael II.
1000 – The foundation of the Kingdom of Hungary: Hungary is established as a Christian kingdom by Stephen I of Hungary.
1013 – Sweyn Forkbeard takes control of the Danelaw and is proclaimed king of England.
1025 – Coronation of Mieszko II Lambert as king of Poland.
1046 – Henry III is crowned Holy Roman Emperor by Pope Clement II.
1066 – William the Conqueror, Duke of Normandy is crowned king of England, at Westminster Abbey, London.
1076 – Coronation of Bolesław II the Generous as king of Poland.
1100 – Baldwin of Boulogne is crowned the first King of Jerusalem in the Church of the Nativity in Bethlehem.
1130 – Count Roger II of Sicily is crowned the first king of Sicily.
1261 – Eleven-year-old John IV Laskaris of the restored Eastern Roman Empire is deposed and blinded by orders of his co-ruler Michael VIII Palaiologos.
1492 – The carrack Santa María, commanded by Christopher Columbus, runs onto a reef off Haiti due to an improper watch.
1553 – Battle of Tucapel: Mapuche rebels under Lautaro defeat the Spanish conquistadors and executes the governor of Chile, Pedro de Valdivia.
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36 – Forces of Emperor Guangwu of the Eastern Han, under the command of Wu Han, conquer the separatist Chengjia empire, reuniting China. 274 – A temple to Sol Invictus is dedicated in Rome by Emperor Aurelian. 333 – Roman Emperor Constantine the Great elevates his youngest son Constans to the rank of Caesar. 336 – First documentary sign of Christmas celebration in Rome. 350 – Vetranio meets Constantius II at Naissus (Serbia) and is forced to abdicate his imperial title. Constantius allows him to live as a private citizen on a state pension.
1154 – Henry II of England is crowned at Westminster Abbey. 1187 – Pope Clement III is elected. 1490 – Anne, Duchess of Brittany, is married to Maximilian I, Holy Roman Emperor by proxy. 1562 – The Battle of Dreux takes place during the French Wars of Religion. 1606 – The ships , , and depart England carrying settlers who founded, at Jamestown, Virginia, the first of the thirteen colonies that became the United States. 1675 – The Great Swamp Fight, a pivotal battle in King Philip's War, gives the English settlers a bitterly won victory.
491 – Flavius Anastasius becomes Byzantine emperor, with the name of Anastasius I. 1241 – Batu Khan defeats Béla IV of Hungary at the Battle of Mohi. 1512 – War of the League of Cambrai: Franco-Ferrarese forces led by Gaston de Foix and Alfonso I d'Este win the Battle of Ravenna against the Papal-Spanish forces. 1544 – Italian War of 1542–46: A French army defeats Habsburg forces at the Battle of Ceresole, but fails to exploit its victory.
Covers injective modules, Ox-modules, and their relevance in algebraic structures, emphasizing their importance in resolving acyclic resolutions and computing cohomology.