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Simple semigroup graded rings
University West, Department of Engineering Science, Division of Mechanical Engineering and Natural Sciences.ORCID iD: 0000-0001-6594-7041
Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden.
2015 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 14, no 7Article in journal (Refereed) Published
Abstract [en]

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 nonzero elements of eGe form a hypercentral group and R-e has a nonzero idempotent f, then R is simple if and only if it is graded simple and the center of the corner subring fR(eGe)f is a field. This is a generalization of a result of 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 Goncalves’. We also point out how Jespers’ result immediately implies a generalization of a simplicity result, recently obtained by Baraviera, Cortes and Soares, for crossed products by twisted partial actions.

Place, publisher, year, edition, pages
2015. Vol. 14, no 7
Keyword [en]
Semigroup graded ring, partial skew group ring, simplicity
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hv:diva-7623DOI: 10.1142/S0219498815501029ISI: 000353552200006Scopus ID: 2-s2.0-84928555107OAI: oai:DiVA.org:hv-7623DiVA: diva2:815396
Available from: 2015-05-30 Created: 2015-05-30 Last updated: 2017-12-04Bibliographically approved

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