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Simple graded rings, non-associative crossed products and Cayley-Dickson doublings
University West, Sweden.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
(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.

Keyword [en]
non-associative ring, group graded ring, simplicity, non-associative crossed product, Cayley algebra
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:bth-13259OAI: oai:DiVA.org:bth-13259DiVA: diva2:1037646
Available from: 2016-10-17 Created: 2016-10-17 Last updated: 2016-11-08Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • modern-language-association-8th-edition
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