Antonio Fernández López, Eulalia García Rus, Ottmar Loos
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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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.
Key concepts: Annihilator, Socle, Mathematics, Principal (computer security), Element (criminal law), Ideal (ethics), Algebra over a field, Pure mathematics