Nonassociative cyclic extensions of fields and central simple algebras

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 d...

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Main Authors: Brown, C., Pumpluen, S.
Format: Article
Published: Elsevier 2018
Subjects:
Online Access:https://eprints.nottingham.ac.uk/53113/
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author Brown, C.
Pumpluen, S.
author_facet Brown, C.
Pumpluen, S.
author_sort Brown, C.
building Nottingham Research Data Repository
collection Online Access
description 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.
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spelling nottingham-531132020-05-04T19:47:15Z https://eprints.nottingham.ac.uk/53113/ Nonassociative cyclic extensions of fields and central simple algebras Brown, C. Pumpluen, S. 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. Elsevier 2018-07-25 Article PeerReviewed 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) Skew polynomial Ore polynomial cyclic algebra cyclic extension
spellingShingle Skew polynomial
Ore polynomial
cyclic algebra
cyclic extension
Brown, C.
Pumpluen, S.
Nonassociative cyclic extensions of fields and central simple algebras
title Nonassociative cyclic extensions of fields and central simple algebras
title_full Nonassociative cyclic extensions of fields and central simple algebras
title_fullStr Nonassociative cyclic extensions of fields and central simple algebras
title_full_unstemmed Nonassociative cyclic extensions of fields and central simple algebras
title_short Nonassociative cyclic extensions of fields and central simple algebras
title_sort nonassociative cyclic extensions of fields and central simple algebras
topic Skew polynomial
Ore polynomial
cyclic algebra
cyclic extension
url https://eprints.nottingham.ac.uk/53113/