The Zelmanov approach to Jordan homomorphisms of associative algebras

Abstract

Zelmanov's work on prime Jordan algebras leads to an idempotent-free version of Martindale's Theorem on the extension of Jordan homomorphisms and derivations from the hermitian elements H( R, *) of an associative algebra of degree >2 with involution to associative homomorphisms and derivations on R. The condition that J = H( R, *) be of degree >2 is replaced by the intrinsic condition that J = Z( J) ⊂ H( A, *) consist entirely of values of Zelmanov polynomials.