Simplicity of Partial Skew Group Rings of Abelian Groups

Canadian mathematical bulletin

Daniel Gonçalves¹ 

[1] Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis, 88040-900, Brasil

关键词: partial skew group rings;    simple rings;    partial actions;    abelian groups;   

DOI  :  10.4153/CMB-2014-011-1

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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 $Astar_{alpha} G$ is simple if and only if $A$ is$G$-simple and the center of the corner $edelta_0 (Astar_{alpha} G)e delta_0$ is a field for all $ein E$. We apply the result tocharacterize simplicity of partial skew group rings in two cases,namely for partial skew group rings arising from partial actions byclopen subsets of a compact set and partial actions on the set level.

【 授权许可】

Unknown