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Keywords:
group rings; normalized units; nilpotents; idempotents; decompositions; abelian groups
group rings; normalized units; nilpotents; idempotents; decompositions; abelian groups
Summary:
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. Québec, 2009].
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