Prime algebras connected with monsters

We study the overalgebras and the ideals of the Jordan algebras possessing prime $(-1,1)$-envelopings. If a Jordan algebra possesses a prime nonassociative $(-1,1)$-enveloping then we prove that it is also prime; furthermore, its every ideal is a prime algebra. In particular, the overalgebras and metaideals of Jordan monsters are prime.