JB algebras with an exceptional ideal.
JB*-triples have Pelczynski's Property V.
Jordan homomorphisms in proper JCQ-triples.
Jordan polynomials can be analytically recognized
We prove that there exists a real or complex central simple associative algebra M with minimal one-sided ideals such that, for every non-Jordan associative polynomial p, a Jordan-algebra norm can be given on M in such a way that the action of p on M becomes discontinuous.