Autour des algèbres de Bernstein. (About Bernstein algebras)
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).
scientific article; zbMATH DE number 4057744