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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
Åpne denne publikasjonen i ny fane eller vindu >>Epsilon-strongly graded rings, separability and semisimplicity
2018 (engelsk)Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 514, nr Nov., s. 1-24Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
Academic Press, 2018
Emneord
group graded ring, partial crossed product, separable, semisimple, Frobenius
HSV kategori
Identifikatorer
urn:nbn:se:bth-12922 (URN)10.1016/j.jalgebra.2018.08.002 (DOI)000445848900001 ()
Tilgjengelig fra: 2016-08-18 Laget: 2016-08-18 Sist oppdatert: 2018-10-11bibliografisk kontrollert
Nystedt, P. & Öinert, J.Simple graded rings, non-associative crossed products and Cayley-Dickson doublings.
Åpne denne publikasjonen i ny fane eller vindu >>Simple graded rings, non-associative crossed products and Cayley-Dickson doublings
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
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.

Emneord
non-associative ring, group graded ring, simplicity, non-associative crossed product, Cayley algebra
HSV kategori
Identifikatorer
urn:nbn:se:bth-13259 (URN)
Tilgjengelig fra: 2016-10-17 Laget: 2016-10-17 Sist oppdatert: 2016-11-08bibliografisk kontrollert
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ORCID-id: ORCID iD iconorcid.org/0000-0001-6594-7041