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.
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Pumplün, S. Nonassociative Differential Extensions of Characteristic \(\varvec{p}\) . Results Math 72, 245–262 (2017). https://doi.org/10.1007/s00025-017-0656-x
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DOI: https://doi.org/10.1007/s00025-017-0656-x
Mathematics Subject Classification
- Primary: 17A35
- Secondary: 17A60
- 17A36
Keywords
- Differential polynomial ring
- skew polynomial
- differential polynomial
- differential operator
- differential algebra
- nonassociative division algebra