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Trivial Units for Group Rings with G-adapted Coefficient Rings

Published online by Cambridge University Press:  20 November 2018

Allen Herman
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina, SK, S4S 0A2 e-mail: aherman@math.uregina.ca
Yuanlin Li
Affiliation:
Department of Mathematics, Brock University, St. Catharines, ON, L2S 3A1 e-mail: Yuanlin.Li@brocku.ca
M. M. Parmenter
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, A1C 5S7 e-mail: michael1@math.mun.ca
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Abstract

For each finite group $G$ for which the integral group ring $\mathbb{Z}G$ has only trivial units, we give ring-theoretic conditions for a commutative ring $R$ under which the group ring $RG$ has nontrivial units. Several examples of rings satisfying the conditions and rings not satisfying the conditions are given. In addition, we extend a well-known result for fields by showing that if $R$ is a ring of finite characteristic and $RG$ has only trivial units, then $G$ has order at most 3.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2005

References

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