Morphic and principal-ideal group rings

Details Morphic and principal-ideal group rings Morphic and principal-ideal group rings

2006-12-01

arxiv.org/abs/math/0612037v1

J. Algebra 318 (2007) 393-411

Mathematics

Rings and Algebras

21 pages

Scientific paper

10.1016/j.jalgebra.2007.09.005

We observe that the class of left and right artinian left and right morphic rings agrees with the class of artinian principal ideal rings. For $R$ an artinian principal ideal ring and $G$ a group, we characterize when $RG$ is a principal ideal ring; for finite groups $G$, this characterizes when $RG$ is a left and right morphic ring. This extends work of Passman, Sehgal and Fisher in the case when $R$ is a field, and work of Chen, Li, and Zhou on morphic group rings.

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