Abstract:Suppose $R$ is a commutative unital ring and $G$ is an abelian group. We give a general criterion only in terms of $R$ and $G$ when all normalized units in the commutative group ring $RG$ are $G$-nilpotent. This extends recent results published in [Extracta Math., 2008--2009] and [Ann. Sci. Math. Qu\'ebec, 2009].
Keywords: group rings, normalized units, nilpotents, idempotents, decompositions, abelian groups
AMS Subject Classification: 16S34 16U60 20K10 20K20 20K21