Nonassociative differential extensions of characteristic p

Pumpluen, Susanne

Abstract

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.

Citation

Pumpluen, S. (2017). Nonassociative differential extensions of characteristic p. Results in Mathematics, 72(1-2), https://doi.org/10.1007/s00025-017-0656-x

• Journal Article Type: Article
• Acceptance Date: Feb 2, 2017
• Online Publication Date: Feb 13, 2017
• Publication Date: Sep 30, 2017
• Deposit Date: Feb 7, 2017
• Publicly Available Date: Feb 13, 2017
• Journal: Results in Mathematics
• Print ISSN: 1422-6383
• Electronic ISSN: 1420-9012
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 72
• Issue: 1-2
• DOI: https://doi.org/10.1007/s00025-017-0656-x
• Keywords: Differential polynomial ring, Skew polynomial, Differential polynomial, Differential operator, Differential algebra, Nonassociative division algebra
• Public URL: https://nottingham-repository.worktribe.com/output/885788
• Publisher URL: http://link.springer.com/article/10.1007%2Fs00025-017-0656-x