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Nonassociative differential extensions of characteristic p

Pumpluen, Susanne

Authors

Susanne Pumpluen susanne.pumpluen@nottingham.ac.uk



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.

Journal Article Type Article
Publication Date Sep 30, 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
APA6 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
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
Publisher URL http://link.springer.com/article/10.1007%2Fs00025-017-0656-x
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0





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