Christian Brown
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. |
Contract Date | Jul 24, 2018 |
Files
GeneralizedCyclicExtsJPAA.pdf
(293 Kb)
PDF
Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0
You might also like
How to obtain division algebras used for fast-decodable space-time block codes
(2014)
Journal Article
Tensor products of nonassociative cyclic algebras
(2015)
Journal Article
The automorphisms of Petit's algebras
(2017)
Journal Article
Nonassociative differential extensions of characteristic p
(2017)
Journal Article
Downloadable Citations
About Repository@Nottingham
Administrator e-mail: discovery-access-systems@nottingham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search