The Zirid dynasty rejects Shi'ite obedience and Fatimid domination, and recognizes the Abbasids as their overlords.
March 17 – Battle of Olivento (near the river Olivento in Apulia in the Catepanate of Italy): Normans and Lombards, led by William Iron Arm, are victorious against the Byzantine Empire's army, led by Michael Dokeianos, Catepan of Italy, and Harald Hardrada.
May 4 – Battle of Montemaggiore (by the river Ofanto near Cannae in Apulia in the Catepanate of Italy): Normans and Lombards, led by William Iron Arm, are again victorious against the Byzantine forces, led by Michael Dokeianos, Catepan of Italy.
December 10 – Zoe Porphyrogenita, Empress Consort of Byzantium, elevates her adoptive son to the throne of the Byzantine Empire, as Michael V Kalaphates, on the death of her husband Michael IV the Paphlagonian.
The inland city of Worcester in England rebels against the naval taxes of King Harthacnut.
Edward the Confessor returns from exile in Normandy, to become the heir of his half-brother Harthacnut, as King of England. He reduces the Navy from 60 to 32 ships this year, due to the tax burden.
The number of enlisted soldiers in the Song Dynasty Chinese military reaches well over 1,250,000 troops, an increase since 1022, when there were a million soldiers.
December 10 – Michael IV, Byzantine Emperor (b. 1010)
Year 1041 (MXLI) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar.
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