Algebras whose right nucleus is a central simple algebra
We generalize Amitsur's construction of central simple algebras over a field F which are split by field extensions possessing a derivation with field of constants F to nonassociative algebras: for every central division algebra D over a field F of characteristic zero there exists an infinite-di...
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| Format: | Article |
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Elsevier
2018
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| Online Access: | https://eprints.nottingham.ac.uk/45589/ |
| _version_ | 1848797161677914112 |
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| author | Pumpluen, Susanne |
| author_facet | Pumpluen, Susanne |
| author_sort | Pumpluen, Susanne |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We generalize Amitsur's construction of central simple algebras over a field F which are split by field extensions possessing a derivation with field of constants F to nonassociative algebras: for every central division algebra D over a field F of characteristic zero there exists an infinite-dimensional unital nonassociative algebra whose right nucleus is D and whose left and middle nucleus are a field extension K of F splitting D, where F is algebraically closed in K. We then give a short direct proof that every p-algebra of degree m, which has a purely inseparable splitting field K of degree m and exponent one, is a differential extension of K and cyclic. We obtain finite-dimensional division algebras over a field F of characteristic p > 0 whose right nucleus is a division p-algebra. |
| first_indexed | 2025-11-14T19:59:29Z |
| format | Article |
| id | nottingham-45589 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:59:29Z |
| publishDate | 2018 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-455892020-05-04T19:50:25Z https://eprints.nottingham.ac.uk/45589/ Algebras whose right nucleus is a central simple algebra Pumpluen, Susanne We generalize Amitsur's construction of central simple algebras over a field F which are split by field extensions possessing a derivation with field of constants F to nonassociative algebras: for every central division algebra D over a field F of characteristic zero there exists an infinite-dimensional unital nonassociative algebra whose right nucleus is D and whose left and middle nucleus are a field extension K of F splitting D, where F is algebraically closed in K. We then give a short direct proof that every p-algebra of degree m, which has a purely inseparable splitting field K of degree m and exponent one, is a differential extension of K and cyclic. We obtain finite-dimensional division algebras over a field F of characteristic p > 0 whose right nucleus is a division p-algebra. Elsevier 2018-09 Article PeerReviewed Pumpluen, Susanne (2018) Algebras whose right nucleus is a central simple algebra. Journal of Pure and Applied Algebra, 222 (9). pp. 2773-2783. ISSN 0022-4049 https://www.sciencedirect.com/science/article/pii/S0022404917302566 doi:10.1016/j.jpaa.2017.10.019 doi:10.1016/j.jpaa.2017.10.019 |
| spellingShingle | Pumpluen, Susanne Algebras whose right nucleus is a central simple algebra |
| title | Algebras whose right nucleus is a central simple algebra |
| title_full | Algebras whose right nucleus is a central simple algebra |
| title_fullStr | Algebras whose right nucleus is a central simple algebra |
| title_full_unstemmed | Algebras whose right nucleus is a central simple algebra |
| title_short | Algebras whose right nucleus is a central simple algebra |
| title_sort | algebras whose right nucleus is a central simple algebra |
| url | https://eprints.nottingham.ac.uk/45589/ https://eprints.nottingham.ac.uk/45589/ https://eprints.nottingham.ac.uk/45589/ |