Morphic and principal-ideal group rings
Copyright policy )Morphic and principal-ideal group rings
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.
21 pages
Skew polynomial ring, principal ideal rings, Algebra and Number Theory, Group rings, Artinian rings, Principal ideal ring, Group rings of infinite groups and their modules (group-theoretic aspects), group rings, Mathematics - Rings and Algebras, 16E50, 16U99, 16S34, annihilators, Artinian rings and modules (associative rings and algebras), morphic rings, Rings and Algebras (math.RA), Artinian ring, Morphic ring, FOS: Mathematics, Divisibility, noncommutative UFDs, Group ring, Annihilator
Skew polynomial ring, principal ideal rings, Algebra and Number Theory, Group rings, Artinian rings, Principal ideal ring, Group rings of infinite groups and their modules (group-theoretic aspects), group rings, Mathematics - Rings and Algebras, 16E50, 16U99, 16S34, annihilators, Artinian rings and modules (associative rings and algebras), morphic rings, Rings and Algebras (math.RA), Artinian ring, Morphic ring, FOS: Mathematics, Divisibility, noncommutative UFDs, Group ring, Annihilator
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