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The Periodic Radical of Group Rings and Incidence Algebras

Published online by Cambridge University Press:  20 November 2018

M. M. Parmenter ,
E. Spiegel  and
P. N. Stewart
M. M. Parmenter
Affiliation:
Department of Mathematics and Statistics Memorial University of Newfoundland St. John’s, Newfoundland A1C 5S7
E. Spiegel
Affiliation:
Department of Mathematics University of Connecticut Storrs, Connecticut 06269 U.S.A.
P. N. Stewart
Affiliation:
Department of Mathematics, Statistics and Computing Science Dalhousie University Halifax, Nova Scotia B3H 3J5
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Abstract

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Let $R$ be a ring with 1 and $P(R)$ the periodic radical of $R$. We obtain necessary and sufficient conditions for $P(\text{RG})=0$ when $\text{FG}$ is the group ring of an $\text{FC}$ group $G$ and $R$ is commutative. We also obtain a complete description of $P\left( I(X,R) \right)$ when $I(X,R)$ is the incidence algebra of a locally finite partially ordered set $X$ and $R$ is commutative.

Keywords

16S3416S9916N99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 4 , 01 December 1998 , pp. 481 - 487
Copyright
Copyright © Canadian Mathematical Society 1998

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