Polynomial Identities and Nonidentities of Split Jordan Pairs

We show that split Jordan pairs over rings without 2-torsion can be distinguished by polynomial identities with integer coefficients. In particular, this holds for simple finite-dimensional Jordan pairs over algebraically closed fields of characteristic not 2. We also generalize results of Drensky and Racine and of Rached and Racine on polynomial identities of, respectively, Jordan algebras and Jordan triple systems.