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Simplicity of Partial Skew Group Rings of Abelian Groups

Published online by Cambridge University Press:  20 November 2018

Daniel Gonçalves
Daniel Gonçalves*
Affiliation:
Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis, 88040-900, Brasil e-mail: daemig@gmail.com
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Abstract

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Let $A$ be a ring with local units, $E$ a set of local units for $A$, $G$ an abelian group, and $\alpha$ a partial action of $G$ by ideals of $A$ that contain local units. We show that $\text{A}\,{{\star }_{\alpha }}\,G$ is simple if and only if $A$ is $G$-simple and the center of the corner $e{{\delta }_{0}}\left( \text{A}\,{{\star }_{\alpha }}\,G \right)e{{\delta }_{0}}$ is a field for all $e\,\in \,E$. We apply the result to characterize simplicity of partial skew group rings in two cases, namely for partial skew group rings arising from partial actions by clopen subsets of a compact set and partial actions on the set level.

Keywords

16S3537B05partial skew group ringssimple ringspartial actionsabelian groups
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 3 , 01 September 2014 , pp. 511 - 519
Copyright
Copyright © Canadian Mathematical Society 2014

References

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