Simplicity of Partial Skew Group Rings of Abelian Groups

Gonçalves, Daniel

Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 511-519

Résumé

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.

Détail

DOI : 10.4153/CMB-2014-011-1

Mots-clés : 16S35, 37B05, partial skew group rings, simple rings, partial actions, abelian groups