Kemer, A; Averyanov, I. Some problems in PI-theory (Advances in algebra and combinatorics).

This paper is devoted to a review of some of the most significant results obtained in the theory of polynomial identities and trace polynomial identities. Some of the most important problems in this area concern the relation between identities in characteristic 0 and p>0 and the classification of prime varieties. Here the authors present their achievements on the subject and makes some conjectures. Among others they give results on the classification of the multilinear identities of the prime subvarieties of the variety generated by the algebra of 2X2 matrices over a field of positive characteristic.