Local and Subquotient Inheritance of Simplicity in Jordan Systems

In this paper we prove that the local algebras of a simple Jordan pair are simple. Jordan pairs all of whose local algebras are simple are also studied, showing that they have a nonzero simple heart, which is described in terms of powers of the original pair. Similar results are given for Jordan triple systems and algebras. Finally, we characterize the inner ideals of a simple pair which determine simple subquotients, answering the question posed by O. Loos and E. Neher in ["Complementation of Inner Ideals in Jordan Pairs", J. Algebra 166 (2) (1994), 255-295].

(To appear in J. Algebra)


J. A. Anquela <anque@pinon.ccu.uniovi.es> T. Cortés <cortes@pinon.ccu.uniovi.es>