Algebras whose right nucleus is a central simple algebra

Pumpluen, Susanne (2017) Algebras whose right nucleus is a central simple algebra. Journal of Pure and Applied Algebra . ISSN 0022-4049 (In Press)

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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.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1016/j.jpaa.2017.10.019
Depositing User: Eprints, Support
Date Deposited: 08 Sep 2017 11:46
Last Modified: 26 Oct 2017 15:53

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