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Epsilon-strongly graded rings, separability and semisimplicity
University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.ORCID iD: 0000-0001-6594-7041
Blekinge Institute of Technology, Department of Mathematics and Natural Sciences, Karlskrona, SE-37179, Sweden.
Universidad Industrial de Santander, Escuela de Matemáticas, Carrera 27 Calle 9, Edificio Camilo Torres Apartado de correos 678, Bucaramanga, Colombia.
2018 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 514, 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 class of strongly graded rings and the class of unital partial crossed products. We determine precisely when an epsilon-strongly graded ring is separable over its principal component. Thereby, we simultaneously generalize a result for strongly group graded rings by Nǎstǎsescu, Van den Bergh and Van Oystaeyen, and a result for unital partial crossed products by Bagio, Lazzarin and Paques. We also show that the class of unital partial crossed products appears in the class of epsilon-strongly graded rings in a fashion similar to how the classical crossed products present themselves in the class 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 Simón concerning when graded rings can be presented as partial crossed products. We also provide some interesting classes of examples of separable epsilon-strongly graded rings, with finite as well as infinite grading groups. In particular, we obtain an answer to a question raised by Le Bruyn, Van den Bergh and Van Oystaeyen in 1988. © 2018 Elsevier Inc.

Place, publisher, year, edition, pages
2018. Vol. 514, p. 1-24
Keywords [en]
Group graded ring, Partial crossed product, SeparableSemisimple, Frobenius
National Category
Mathematics Algebra and Logic
Research subject
ENGINEERING, Mathematics
Identifiers
URN: urn:nbn:se:hv:diva-12978DOI: 10.1016/j.jalgebra.2018.08.002ISI: 000445848900001Scopus ID: 2-s2.0-85051634856OAI: oai:DiVA.org:hv-12978DiVA, id: diva2:1259245
Available from: 2018-10-29 Created: 2018-10-29 Last updated: 2019-05-28Bibliographically approved

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