Herstein's Theorems and Simplicity of Hermitian Jordan Systems

In this paper we extend Herstein's first construction relating associative and Jordan ideals to pairs and triple systems. As a consequence we show that an associative pair or triple systems is simple if and only if its Jordan symmetrization is simple. We also generalize Herstein's second construction to ample subsystems of associative algebras, pairs and triple systems, which provides information on their simplicity when the associative structure is simple.

(To appear in J. Algebra)

J. A. Anquela <anque@pinon.ccu.uniovi.es> T. Cortes <cortes@pinon.ccu.uniovi.es> E. Garcia <egarciag@mat.ucm.es>