Annihilators of elements of the socle of a jordan algebra

Antonio Fernández López Departamento de Algebra, Universidad de Málaga, Facultad de Ciencias, Geometrfay Topologia, Malaga, 29071, Spain

Eulalia García Rus Departamento de Algebra, Universidad de Málaga, Facultad de Ciencias, Geometrfay Topologia, Malaga, 29071, Spain

Ottmar Loos Institut fur Mathematik der Universitat Innsbruck, Innsbruck, A-6020, AustriaTechnikerstrape 25/7

Abstract

The double annihilator of any element in the socle of a nondegenerate quadratic Jordan algebra coincides with the principal inner ideal generated by this element. Since the socle satisfies dec on principal inner ideals, it also satisfies ace on annihilators of principal inner ideals.

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