Nonassociative cyclic extensions of fields and central simple algebras

Brown, Christian; Pumpluen, Susanne

Abstract

We define nonassociative cyclic extensions of degree m of both fields andcentral simple algebras over fields. If a suitable field contains a primitive mth (resp., qth) root of unity, we show that suitable nonassociative generalized cyclic division algebras yield nonassociative cyclic extensions of degree m (resp., qs). Some of Amitsur's classical results on non-commutative associative cyclic extensions of both fields and central simple algebras are obtained as special cases.

Citation

Brown, C., & Pumpluen, S. (2019). Nonassociative cyclic extensions of fields and central simple algebras. Journal of Pure and Applied Algebra, 223(6), 2401-2412. https://doi.org/10.1016/j.jpaa.2018.08.018

• Journal Article Type: Article
• Acceptance Date: Jul 25, 2018
• Online Publication Date: Aug 28, 2018
• Publication Date: 2019-06
• Deposit Date: Jul 24, 2018
• Publicly Available Date: Aug 29, 2019
• Journal: Journal of Pure and Applied Algebra
• Print ISSN: 0022-4049
• Electronic ISSN: 0022-4049
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 223
• Issue: 6
• Pages: 2401-2412
• DOI: https://doi.org/10.1016/j.jpaa.2018.08.018
• Keywords: Skew polynomial, Ore polynomial, cyclic algebra, cyclic extension
• Public URL: https://nottingham-repository.worktribe.com/output/947682
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0022404918302159?via%3Dihub
• Additional Information: This article is maintained by: Elsevier; Article Title: Nonassociative cyclic extensions of fields and central simple algebras; Journal Title: Journal of Pure and Applied Algebra; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.jpaa.2018.08.018; Content Type: article; Copyright: © 2018 Elsevier B.V. All rights reserved.