Morphic and principal-ideal group rings

Abstract

For R an artinian ring and G a group, we characterize when RG is a principal ideal ring. In the case when G is finite (and R artinian), this yields a characterization of when RG is a left and right morphic ring. This extends work done by Passman, Sehgal and Fisher on principal ideal group rings when the coefficient ring is a field, and work of Chen, Li, and Zhou on morphic group rings.