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Simple graded rings, nonassociative crossed products and Cayley-Dickson doublings
University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.ORCID iD: 0000-0001-6594-7041
Blekinge Tekniska Högskola, Karlskrona, Sweden.
2019 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, article id 2050231Article in journal (Refereed) Epub ahead of print
Abstract [en]

e show that if a nonassociative 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 to a nonassociative setting. By applying this result to nonassociative crossed products, we obtain nonassociative analogues of results by Bell, Jordan and Voskoglou. We also apply our result to Cayley-Dickson doublings, thereby obtaining a new proof of a classical result by McCrimmon. © 2020 World Scientific Publishing Company.

Place, publisher, year, edition, pages
2019. article id 2050231
Keywords [en]
Cayley algebra, group graded ring, nonassociative crossed product, Nonassociative ring, simplicity
National Category
Algebra and Logic
Research subject
ENGINEERING, Mathematics
Identifiers
URN: urn:nbn:se:hv:diva-14872DOI: 10.1142/S021949882050231XScopus ID: 2-s2.0-85076527806OAI: oai:DiVA.org:hv-14872DiVA, id: diva2:1389168
Available from: 2020-01-29 Created: 2020-01-29 Last updated: 2020-01-29Bibliographically approved

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