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 which local algebras are simple are also studie d, showing that they have a nonzero simple heart, which is described in ter ms of powers of the original pair. Similar results are given for Jordan tri ple systems and algebras. Finally, we characterize the inner ideals of a si mple pair which determine simple subquotients, answering the question posed by O. Loos and E. Neher (1994, J. Algebra 166, 255-295). (C) zool Academic Press.