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Algebras whose right nucleus is a central simple algebra

Pumpluen, Susanne

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Abstract

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.

Journal Article Type Article
Acceptance Date Sep 8, 2017
Online Publication Date Oct 23, 2017
Publication Date Sep 1, 2018
Deposit Date Sep 8, 2017
Publicly Available Date Oct 24, 2018
Journal Journal of Pure and Applied Algebra
Print ISSN 0022-4049
Electronic ISSN 0022-4049
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 222
Issue 9
DOI https://doi.org/10.1016/j.jpaa.2017.10.019
Public URL https://nottingham-repository.worktribe.com/output/960758
Publisher URL https://www.sciencedirect.com/science/article/pii/S0022404917302566

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