Bernstein algebras
type: Item
instance of: scholarly article
title: Bernstein algebras
zbMATH Open document ID: 0597.17014
DOI: 10.1007/BF01189631
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: It is shown that the decomposition of a Bernstein algebra with respect to an idempotent is nothing else but the Peirce decomposition which is known for power associative algebras with idempotent, especially for Jordan algebras with idempotent. Futhermore all idempotents of a Bernstein algebra are principal and primitive. For every Bernstein algebra a necessary and sufficient condition to be a Jordan algebra is given. All trivial Bernstein algebras are Jordan algebras, and beyond this, they are special Jordan algebras. Furthermore all normal Bernstein algebras are Jordan algebras.
Mathematics Subject Classification ID: 17D92
Mathematics Subject Classification ID: 17A60
Mathematics Subject Classification ID: 17C50
zbMATH DE Number: 3961915
zbMATH Keywords: decomposition
zbMATH Keywords: Bernstein algebra
zbMATH Keywords: idempotent
zbMATH Keywords: Peirce decomposition
zbMATH Keywords: Jordan algebra
author: Angelika Woerz-Busekros
MaRDI profile type: Publication
cites work: Sur Les Algèbres de Bernstein
cites work: Jordan algebras arising in population genetics
cites work: Genetic Algebras Satisfying Bernstein's Stationarity Principle
cites work: Algebraic Methods in Evolutionary Genetics
cites work: Q5522244
cites work: Q3869125
cites work: Further Remarks on Bernstein Algebras
full work available at URL: https://doi.org/10.1007/bf01189631
OpenAlex ID: W4229884089
description: scientific article; zbMATH DE number 3961915