Semi-prime Bernstein algebras
type: Item
instance of: scholarly article
title: Semi-prime Bernstein algebras
zbMATH Open document ID: 0643.17018
DOI: 10.1007/BF01237566
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: Let \(A\) be a nonassociative algebra over a field \(K\). \(A\) is called semiprime if it satisfies the following condition: If \(I\) is an ideal of \(A\) and \(I^2=0\), then \(I=0\). \(A\) is called a Bernstein algebra if \(A\) is commutative and has a nontrivial algebra homomorphism \(w: A\to K\) which satisfies the identity \(x^2x^2=w(x)^2x^2\) for all \(x\in A\). The authors prove that: (i) a semiprime Bernstein algebra is a Jordan algebra, (ii) a finitely generated semiprime Bernstein algebra is a field, and (iii) if \(A\) is a finitely generated Bernstein algebra, then the kernel of \(w\) is solvable. The proofs require characteristic different from two.
Mathematics Subject Classification ID: 17D92
Mathematics Subject Classification ID: 17A30
Mathematics Subject Classification ID: 17C99
zbMATH DE Number: 4047924
zbMATH Keywords: semiprime Bernstein algebra
zbMATH Keywords: Jordan algebra
author: Irvin Roy Hentzel
author: Luiz Antonio Peresi
reviewed by: Irvin Roy Hentzel
MaRDI profile type: Publication
cites work: Characterisations of Genetic Algebras
cites work: Genetic Algebras Satisfying Bernstein's Stationarity Principle
cites work: Bernstein algebras
cites work: Further Remarks on Bernstein Algebras
cites work: Q3947798
full work available at URL: https://doi.org/10.1007/bf01237566
OpenAlex ID: W1977089827
description: scientific article; zbMATH DE number 4047924