The Annals of Tigernach record that “Murchad son of Diarmait son of Mael na mbó” invaded “Mann…and defeated Ragnall´s son” in 1061.
The Annals of Ulster record the death in 1070 of "Murchad son of Diarmait king of Laigin and the foreigners…buried in Áth Cliath”. The Annals of Inisfallen record the death in 1070 of "Murchad son of Diarmiat son of Mael na mBó king of foreigners and Gaedil…in Áth Cliath”. 1