Polynomial preserving maps on certain Jordan algebras

LetB andQ be associative algebras and letS be a Jordan subalgebra ofB. Letf(x ₁,…,x _m ) be a (noncommutative) multilinear polynomial such thatS is closed underf. Letα:S→Q be anf-homomorphism in the sense that it is a linear map preservingf. Under suitable conditions it is shown thatα is essentially given by a ring homomorphism. An analogous theorem forf-derivations is also proved. The proofs rest heavily on results concerning functional identities andd-freeness. The second author was partially supported by a grant from the Ministry of Science of Slovenia.