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Outer Partial Actions and Partial Skew Group Rings
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- Journal:
- Canadian Journal of Mathematics / Volume 67 / Issue 5 / 01 October 2015
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1144-1160
- Print publication:
- 01 October 2015
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- Article
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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.
