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Nystedt, P., Öinert, J. & Pinedo, H. (2018). Epsilon-strongly graded rings, separability and semisimplicity. Journal of Algebra, 514(Nov.), 1-24
Open this publication in new window or tab >>Epsilon-strongly graded rings, separability and semisimplicity
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
Keywords
group graded ring, partial crossed product, separable, semisimple, Frobenius
National Category
Algebra and Logic
Identifiers
urn:nbn:se:bth-12922 (URN)10.1016/j.jalgebra.2018.08.002 (DOI)000445848900001 ()
Available from: 2016-08-18 Created: 2016-08-18 Last updated: 2018-10-11Bibliographically approved
Nystedt, P. & Öinert, J.Simple graded rings, non-associative crossed products and Cayley-Dickson doublings.
Open this publication in new window or tab >>Simple graded rings, non-associative crossed products and Cayley-Dickson doublings
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We show that if a non-associative unital ring is graded by a hypercentral group, then the ring is simple if and only if it is graded simple and the center of the ring is a field. Thereby, we extend a result by Jespers from the associative case to the non-associative situation. By applying this result to non-associative crossed products, we obtain non-associative analogues of results by Bell, Jordan and Voskoglou. We also apply this result to Cayley-Dickson doublings, thereby obtaining a new proof of a classical result by McCrimmon.

Keywords
non-associative ring, group graded ring, simplicity, non-associative crossed product, Cayley algebra
National Category
Algebra and Logic
Identifiers
urn:nbn:se:bth-13259 (URN)
Available from: 2016-10-17 Created: 2016-10-17 Last updated: 2016-11-08Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-6594-7041

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