On polynomial identities in associative and Jordan pairs (Q964832)

In this paper the authors prove that a Jordan system (pair or triple system) \(J\) satisfies a polynomial identity (PI) if and only if it satisfies a homotope PI, i.e. a PI which holds in all the homotopes of \(J\). The core of the proof, based on structure theory, is the following analogue of Amitsur's theorem on associative algebras with involution satisfying a *-PI: If \(A\) is a primitive associative pair with involution * such that the Jordan pair of the Hermitian elements \(H(A,{}^*)\) satisfies a PI, then \(A\) is simple of finite capacity. The paper concludes by stating improvements on already-proved Jordan analogues of Kaplansky's and Posner-Rowen's theorems on primitive and prime PI-algebras.