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Simplicity of Partial Skew Group Rings of Abelian Groups

  • Daniel Gonçalves (a1)
Abstract

Let A be a ring with local units, E a set of local units for A, G an abelian group, and α a partial action of G by ideals of A that contain local units. We show that A*α G is simple if and only if A is G-simple and the center of the corner eδ0(A*α Ge)eδ0 is a field for all eE. 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.

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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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