Simple graded rings, non-associative crossed products and Cayley-Dickson doublings
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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.
non-associative ring, group graded ring, simplicity, non-associative crossed product, Cayley algebra
Algebra and Logic
IdentifiersURN: urn:nbn:se:bth-13259OAI: oai:DiVA.org:bth-13259DiVA: diva2:1037646