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Outer Partial Actions and Partial Skew Group Rings

Published online by Cambridge University Press:  20 November 2018

Patrik Nystedt  and
Johan Öinert
Patrik Nystedt
Affiliation:
University West, Department of Engineering Science, SE-46186 Trollhättan, Sweden. e-mail: patrik.nystedt@hv.se
Johan Öinert
Affiliation:
Centre for Mathematical Sciences, P.O. Box 118, Lund University, SE-22100 Lund, Sweden. e-mail: johan.oinert@math.lth.se
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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.

Keywords

16S3516W5037B0537B9954H1554H20outer actionpartial actionminimalitytopological dynamicspartial skew group ringsimplicity
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 5 , 01 October 2015 , pp. 1144 - 1160
Copyright
Copyright © Canadian Mathematical Society 2015

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