2013/08/15 by Patrik Nystedt, Nystedt, Patrik, Johan Öinert +1
Mathematics · #16D25 #16S35 #16U70 #16W50 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16D25 #msc:16S35 #msc:16U70 #msc:16W50
paper · pdf · doi:10.48550/arxiv.1308.3459
9 pages
openalex publication_date 2013/08/15 · arxiv created 2014/09/08 · arxiv updated 2014/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that if R is a, not necessarily unital, ring graded by a semigroup G equipped with an idempotent e such that G is cancellative at e, the non-zero elements of eGe form a hypercentral group and Re has a non-zero idempotent f, then R is simple if and only if it is graded simple and the center of the corner subring f ReGe f is a field. This is a generalization of a result of E. Jespers' on the simplicity of a unital ring graded by a hypercentral group. We apply our result to partial skew group rings and obtain necessary and sufficient conditions for the simplicity of a, not necessarily unital, partial skew group ring by a hypercentral group. Thereby, we generalize a very recent result of D. Gonçalves'. We also point out how E. Jespers' result immediately implies a generalization of a simplicity result, recently obtained by A. Baraviera, W. Cortes and M. Soares, for crossed products by twisted partial actions.