Autour des algèbres de Bernstein. (About Bernstein algebras)
type: Item
instance of: scholarly article
title: Autour des algèbres de Bernstein. (About Bernstein algebras)
zbMATH Open document ID: 0648.17011
DOI: 10.1007/BF01198562
author: María Teresa Alcade
author: Rodolfo Baeza
author: César Burgueño
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: It is proved that a Bernstein K-algebra \(A=Ke\oplus U\oplus V\) is a Jordan algebra if and only if V \(2=(0)\) and \(v(vU)=(0)\) for all v in V. It is studied the orthogonality notion of a Bernstein algebra by proving that if the algebra is not orthogonal, then the dimensions of the subspaces U and V are respectively greater than two and one. It is shown an example of a Bernstein algebra that is not orthogonal of type (4,2).
Mathematics Subject Classification ID: 17D92
Mathematics Subject Classification ID: 17A30
Mathematics Subject Classification ID: 17C99
zbMATH DE Number: 4057744
zbMATH Keywords: Jordan algebra
zbMATH Keywords: orthogonality
zbMATH Keywords: Bernstein algebra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4057744