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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| Format: | Article |
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Elsevier
2018
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| Online Access: | https://eprints.nottingham.ac.uk/53113/ |
| _version_ | 1848798880983941120 |
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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. |
| first_indexed | 2025-11-14T20:26:48Z |
| format | Article |
| id | nottingham-53113 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:26:48Z |
| publishDate | 2018 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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/ |