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# Outer Partial Actions and Partial Skew Group Rings

Published:2015-03-03
Printed: Oct 2015
• Patrik Nystedt,
University West, Department of Engineering Science, SE-46186 Trollh?ttan, Sweden
• Johan Öinert,
Centre for Mathematical Sciences, P.O. Box 118, Lund University, SE-22100 Lund, Sweden
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## Abstract

We extend the classicial 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: outer action, partial action, minimality, topological dynamics, partial skew group ring, simplicity
 MSC Classifications: 16W50 - Graded rings and modules 37B05 - Transformations and group actions with special properties (minimality, distality, proximality, etc.) 37B99 - None of the above, but in this section 54H15 - Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx] 54H20 - Topological dynamics [See also 28Dxx, 37Bxx]

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