Shape identities in train algebras of rank 3
type: Item
instance of: scholarly article
title: Shape identities in train algebras of rank 3
zbMATH Open document ID: 0935.17021
DOI: 10.1007/BF03322021
author: Roberto Costa
author: P. Vicente
author: H. jun. Guzzo
published in: Results in Mathematics
publication date: 2000-05-10T00:00:00Z
review text: The authors consider the possible shape identities satisfied by a commutative baric algebra \((A,\omega)\) over the field \(F\) \((\text{char } F\neq 2)\) that satisfies the identity \(x^3- (1+\gamma) \omega(x)x^2+ \gamma\omega(x)^2 x=0\), where \(\gamma\in F\). These algebras are called train algebras of rank 3. The authors classify train algebras of rank 3 according to their levels, up to level 5. The studying of train algebras of level \(6,7,\dots\) requires more sophisticated computational techniques. Therefore, they do not consider these algebras in this paper.
Mathematics Subject Classification ID: 17D92
zbMATH DE Number: 1294481
zbMATH Keywords: shape identities
zbMATH Keywords: commutative baric algebra
zbMATH Keywords: train algebras of rank 3
reviewed by: A. A. Rakhimov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03322021
OpenAlex ID: W2024093428
description: scientific article; zbMATH DE number 1294481