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arXiv · 1402.3205

Outer partial actions and partial skew group rings

Patrik Nystedt·Johan Öinert
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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.

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Patrik Nystedt, Johan Öinert. 2014-02-13. Outer partial actions and partial skew group rings. https://doi.org/10.4153/cjm-2014-043-8

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