Morphic group rings

An element a in a ring R   is called left morphic if there exists b∈Rb∈R such that lR(a)=RblR(a)=Rb and lR(b)=RalR(b)=Ra, where lR(a)lR(a) denotes the left annihilator of a in R. The ring R is called left morphic if every element of R is left morphic. Left morphic rings have been studied by Nicholson and Sánchez Campos. In this paper, the question of when a group ring is left morphic is discussed in great detail and various morphic group rings are identified.