The Bernstein problem in dimension 5
type: Item
instance of: scholarly article
title: The Bernstein problem in dimension 5
zbMATH Open document ID: 0856.17028
author: Consuelo Martínez
author: Santos González
author: J. Carlos Gutiérrez
published in: Journal of Algebra
publication date: 1997-02-24T00:00:00Z
review text: A Bernstein algebra \(A\) has a Peirce decomposition relative to an idempotent \(e\), given by \(A= \text{Re} (+)U(+)V\). If \(UV+V^2=0\), the algebra is called ``regular''. If \(U^2=0\) the algebra is called ``exceptional''. The authors study the Bernstein algebras with are not regular and not exceptional and are of dimension 5. They first show that Bernstein algebras are not regular and not exceptional if and only if they have a basis \(\{e,u1,u2,v1,v2\}\) and one of six types of multiplication tables. They then classify stochastic not regular not exceptional Bernstein algebras of dimension 5. They give two types of these algebras and show that all such algebras are of one of these two types.
reviewed by: Irvin Roy Hentzel
Mathematics Subject Classification ID: 17D92
zbMATH DE Number: 827371
zbMATH Keywords: regular
zbMATH Keywords: exceptional
zbMATH Keywords: Bernstein algebra
zbMATH Keywords: Peirce decomposition
zbMATH Keywords: idempotent
MaRDI profile type: Publication
full work available at URL: jabr.1995.1323
OpenAlex ID: W2068865316
DOI: 10.1006/JABR.1995.1323
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description: scientific article; zbMATH DE number 827371