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Autour des algèbres de Bernstein. (About Bernstein algebras). (French) Zbl 0648.17011
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).
Reviewer: C.Burgueño

MSC:
17D92 Genetic algebras
17A30 Nonassociative algebras satisfying other identities
17C99 Jordan algebras (algebras, triples and pairs)
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