VARIETY OF BICOMMUTATIVE ALGEBRAS DEFINED BY IDENTITY Γ[(AB)C − 2(BA)C + (CA)B] + Δ[C(BA) − 2C(AB) + B(AC)] = 0

Abstract

One of the important problem of the theory of polynomial identi tites in algebra is describe all varieties of algebras with given system of identities. Our aim is to classify all subvarieties of the variety of bicom mutative algebras. Classifying is usually done in the language of lattices. Of course this problem is equivalent to describing of T-ideals. In order to construct a lattice of subvarieties of given variety of algebras, we need to define the following 1) determine the module structure of Pn(M) over the symmetric group; 2) find for each irreducible Sn-module in Pn(M) a consequence in Pn+1(M).