Degree three, four, and five identities of quadratic algebras
type: Item
instance of: scholarly article
title: Degree three, four, and five identities of quadratic algebras
zbMATH Open document ID: 0915.17003
author: Irvin Roy Hentzel
author: Luiz Antonio Peresi
published in: Journal of Algebra
publication date: 1999-07-05T00:00:00Z
review text: Let \(C\) be a class of nonassociative algebras over a field \(F\). Then the polynomial identity \(f(x_1, \dots, x_n)\) is a special central identity for all algebras in \(C\) if there is an algebra in \(C\) for which \(f(x_1, \dots, x_n)\) is not an identity, but for any \(A\) in \(C\) one has \(f(a_1, \dots, a_n)\in F\) for all \(a_1, \dots, a_n\in A\). Assume that \(\text{char} (F)=0\), or is greater than the degree of the identity considered. The authors determine sets of identities which generate all degree 3, 4 and 5 polynomial identities of quadratic algebras and symmetric quadratic algebras. They also obtain the special central identities of degree 3 and 4, and some results for Jordan algebras of degree 2.
Mathematics Subject Classification ID: 17A45
Mathematics Subject Classification ID: 17A30
Mathematics Subject Classification ID: 17C05
zbMATH DE Number: 1214138
zbMATH Keywords: quadratic algebras
zbMATH Keywords: polynomial identity
zbMATH Keywords: special central identity
zbMATH Keywords: symmetric quadratic algebras
zbMATH Keywords: Jordan algebras of degree 2
MaRDI profile type: Publication
full work available at URL: jabr.1997.7401
OpenAlex ID: W1978171298
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DOI: 10.1006/JABR.1997.7401
description: scientific article; zbMATH DE number 1214138