Prime Quotients of Jordan Systems and Lie Algebras
We show that, unlike alternative algebras, prime quotients
of a nondegenerate Jordan system
or a Lie algebra need not be nondegenerate, even if the original
Jordan system is primitive,
or the Lie algebra is strongly prime, both with nonzero simple
hearts. Nevertheless, for
Jordan systems and Lie algebras directly linked to associative
systems, we prove
that even semiprime quotients are necessarily nondegenerate.