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Outer Partial Actions and Partial Skew Group Rings

Published online by Cambridge University Press:  20 November 2018

Patrik Nystedt
Affiliation:
University West, Department of Engineering Science, SE-46186 Trollhättan, Sweden. e-mail: [email protected]
Johan Öinert
Affiliation:
Centre for Mathematical Sciences, P.O. Box 118, Lund University, SE-22100 Lund, Sweden. e-mail: [email protected]
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Abstract

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We extend the classical notion of an outer action $\alpha $ of a group $G$ on a unital ring $A$ to the case when $\alpha $ is a partial action on ideals, all of which have local units. We show that if $\alpha $ is an outer partial action of an abelian group $G$, then its associated partial skew group ring $A\,{{\star }_{\alpha }}\,G$ is simple if and only if $A$ is $G$-simple. This result is applied to partial skew group rings associated with two different types of partial dynamical systems.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2015

References

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