He is supposedly the source of the history of Brian Boru called Cogad Gáedel re Gallaib (English: The War of the Irish with the Foreigners).
His obit is given in the Annals of the Four Masters as follows- "M1015.7 Macliag, i.e. Muircheartach, son of Cuceartach, chief poet of Ireland at that time, died.
Muircheartach Beag, son of Maelcertach, who has been herding the cows, It is more worthy that he retaliates not,—give him a handful of findraip (corn).
His obit is given in the Annals of Loch Cé as follows- "LC1016.1 Mac Liag, chief poet of Erinn, mortuus est."
Mac Liac i.e. Muirchertach, chief ollamh of Ireland, an excellent man, dies in Inis Gaill Duibh on the Sinna.