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Epsilon-strongly graded rings, separability and semisimplicity
University West, SWE.ORCID iD: 0000-0001-6594-7041
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.ORCID iD: 0000-0001-8095-0820
Industrial University of Santander, COL.
2018 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 514, no Nov., p. 1-24Article in journal (Refereed) Published
Abstract [en]

We introduce the class of epsilon-strongly graded rings and show that it properly contains both the collection of strongly graded rings and the family of unital partial crossed products. We determine when epsilon-strongly graded rings are separable over their principal components. Thereby, we simultaneously generalize a result for strongly group-graded rings by Nastasescu, Van den Bergh and Van Oystaeyen, and a result for unital partial crossed products by Bagio, Lazzarin and Paques. We also show that the family of unital partial crossed products appear in the class of epsilon-strongly graded rings in a fashion similar to how the classical crossed products present themselves in the family of strongly graded rings. Thereby, we obtain, in the special case of unital partial crossed products, a short proof of a general result by Dokuchaev, Exel and Simon concerning when graded rings can be presented as partial crossed products.

Place, publisher, year, edition, pages
Academic Press, 2018. Vol. 514, no Nov., p. 1-24
Keywords [en]
group graded ring, partial crossed product, separable, semisimple, Frobenius
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:bth-12922DOI: 10.1016/j.jalgebra.2018.08.002ISI: 000445848900001OAI: oai:DiVA.org:bth-12922DiVA, id: diva2:953536
Available from: 2016-08-18 Created: 2016-08-18 Last updated: 2018-10-11Bibliographically approved

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Nystedt, PatrikÖinert, Johan

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CiteExportLink to record
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  • apa
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  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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