Identities of special Jordan algebras with finite grading (Q1406368)

The authors study the special Jordan algebras [see \textit{A. I. Shirshov, K. A. Zhevlakov, A. M. Slin'ko} and \textit{I. P. Shestakov}, Nearly associative rings, Nauka, Moscow (1978; Zbl 0445.17001)] that are graded by a commutative semigroup and have only a finite number of nonzero homogeneous components. It is proved that if all subalgebras indexed by idempotents of the semigroup are PI-algebras, then the algebra itself satisfies a nontrivial identity, the degree of which is estimated from above.