Nonassociative cyclic algebras
type: Item
instance of: scholarly article
title: Nonassociative cyclic algebras
zbMATH Open document ID: 1372.17003
author: Andrew Steele
published in: Israel Journal of Mathematics
publication date: 2014-06-25T00:00:00Z
review text: Starting from previous results, in this paper, the author generalises nonassociative quaternion algebras and introduces nonassociative cyclic algebras of degree \(n\), taking the element \(a\) to be outside of the base field \(F\). As a particular case, he considers nonassociative cyclic algebras whith \(L/F\) a cyclic field extension of degree \(3\). He proves that all of these algebras are division algebras for all \(a\in L\backslash F\). This result is generalised for nonassociative cyclic algebras of degree \(n\). He proves that if \(n\) is prime, then a nonassociative cyclic algebra is a division algebra for all \(a\in L\backslash F\). If \(n\) is not prime, if the elements \( \{1,a,a^2,\ldots,a^{n-1}\}\) are linearly independent over \(F\), then the nonassociative cyclic algebras of degree \(n\) is with division.
reviewed by: Cristina Flaut
Mathematics Subject Classification ID: 17A35
zbMATH DE Number: 6308427
zbMATH Keywords: nonassociative algebras
MaRDI profile type: Publication
full work available at URL: s11856-014-0021-7
OpenAlex ID: W2061315961
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DOI: 10.1007/S11856-014-0021-7
description: scientific article; zbMATH DE number 6308427