Nonassociative cyclic extensions of fields and central simple algebras

Brown, C. and Pumpluen, S. (2018) Nonassociative cyclic extensions of fields and central simple algebras. Journal of Pure and Applied Algebra . ISSN 0022-4049 (In Press)

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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.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/947682
Keywords: Skew polynomial, Ore polynomial, cyclic algebra, cyclic extension
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Depositing User: Eprints, Support
Date Deposited: 24 Jul 2018 10:24
Last Modified: 04 May 2020 19:47
URI: http://eprints.nottingham.ac.uk/id/eprint/53113

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