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Regular skew group rings

Part of: Rings and algebras arising under various constructions

Published online by Cambridge University Press:  09 April 2009

Ricardo Alfaro ,
Pere Ara  and
Angel Del Río
Ricardo Alfaro
Affiliation:
Department of Mathematics, University of Michigan-Flint, Flint, MI 48502, U.S.A.
Pere Ara
Affiliation:
Department de Matemàtiques, Universitat Autònoma de Barcelona, (08193) Bellaterra (Barcelona), Spain
Angel Del Río
Affiliation:
Department de Matemàtiqus, Universidad de Murcia, (30001) Murcia, Spain
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Abstract

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Let G be a group acting on a ring R. We study the problem of determining necessary and sufficient conditions in order that the skew group ring RG be von Neumann regular. Complete characterizations are given in some particular situations, including the case where all idempotents of R are central. For a regular ring R admitting a G-invariant pseudo-rank function N, with G finite, we obtain a necessary condition for RG being regular in terms of the induced action of G on the N-completion of R.

MSC classification

Secondary: 16S35: Twisted and skew group rings, crossed products
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 2 , April 1995 , pp. 167 - 182
Copyright
Copyright © Australian Mathematical Society 1995

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