Nonassociative differential extensions of characteristic p
Let F be a field of characteristic p. We define and investigate nonassociative differential extensions of F and of a finite-dimensional central division algebra over F and give a criterium for these algebras to be division. As special cases, we obtain classical results for associative algebras by Am...
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| Format: | Article |
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Springer
2017
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| Online Access: | https://eprints.nottingham.ac.uk/40324/ |
| _version_ | 1848796029331177472 |
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| author | Pumpluen, Susanne |
| author_facet | Pumpluen, Susanne |
| author_sort | Pumpluen, Susanne |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Let F be a field of characteristic p. We define and investigate nonassociative differential extensions of F and of a finite-dimensional central division algebra over F and give a criterium for these algebras to be division. As special cases, we obtain classical results for associative algebras by Amitsur and Jacobson. We construct families of nonassociative division algebras which can be viewed as generalizations of associative cyclic extensions of a purely inseparable field extension of exponent one or a central division algebra. Division algebras which are nonassociative cyclic extensions of a purely inseparable field extension of exponent one are particularly easy to obtain. |
| first_indexed | 2025-11-14T19:41:29Z |
| format | Article |
| id | nottingham-40324 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:41:29Z |
| publishDate | 2017 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-403242020-05-04T19:10:04Z https://eprints.nottingham.ac.uk/40324/ Nonassociative differential extensions of characteristic p Pumpluen, Susanne Let F be a field of characteristic p. We define and investigate nonassociative differential extensions of F and of a finite-dimensional central division algebra over F and give a criterium for these algebras to be division. As special cases, we obtain classical results for associative algebras by Amitsur and Jacobson. We construct families of nonassociative division algebras which can be viewed as generalizations of associative cyclic extensions of a purely inseparable field extension of exponent one or a central division algebra. Division algebras which are nonassociative cyclic extensions of a purely inseparable field extension of exponent one are particularly easy to obtain. Springer 2017-09-30 Article PeerReviewed Pumpluen, Susanne (2017) Nonassociative differential extensions of characteristic p. Results in Mathematics, 72 (1-2). pp. 245-262. ISSN 1420-9012 Differential polynomial ring Skew polynomial Differential polynomial Differential operator Differential algebra Nonassociative division algebra http://link.springer.com/article/10.1007%2Fs00025-017-0656-x doi:10.1007/s00025-017-0656-x doi:10.1007/s00025-017-0656-x |
| spellingShingle | Differential polynomial ring Skew polynomial Differential polynomial Differential operator Differential algebra Nonassociative division algebra Pumpluen, Susanne Nonassociative differential extensions of characteristic p |
| title | Nonassociative differential extensions of characteristic p |
| title_full | Nonassociative differential extensions of characteristic p |
| title_fullStr | Nonassociative differential extensions of characteristic p |
| title_full_unstemmed | Nonassociative differential extensions of characteristic p |
| title_short | Nonassociative differential extensions of characteristic p |
| title_sort | nonassociative differential extensions of characteristic p |
| topic | Differential polynomial ring Skew polynomial Differential polynomial Differential operator Differential algebra Nonassociative division algebra |
| url | https://eprints.nottingham.ac.uk/40324/ https://eprints.nottingham.ac.uk/40324/ https://eprints.nottingham.ac.uk/40324/ |