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# The periodic radical of group rings and incidence algebras

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Published:1998-12-01
Printed: Dec 1998
• M. M. Parmenter
• E. Spiegel
• P. N. Stewart
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## Abstract

Let $R$ be a ring with $1$ and $P(R)$ the periodic radical of $R$. We obtain necessary and sufficient conditions for $P(\RG) = 0$ when $\RG$ is the group ring of an $\FC$ group $G$ and $R$ is commutative. We also obtain a complete description of $P\bigl(I (X, R)\bigr)$ when $I(X,R)$ is the incidence algebra of a locally finite partially ordered set $X$ and $R$ is commutative.
 MSC Classifications: 16S34 - Group rings [See also 20C05, 20C07], Laurent polynomial rings 16S99 - None of the above, but in this section 16N99 - None of the above, but in this section

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