ALGEBRAS SATISFYING THE POLYNOMIAL IDENTITY [x1,x2][x3,x4,x5]=0
Let [Formula: see text] be a field of characteristic zero, and [Formula: see text] the variety of associative unitary algebras defined by the polynomial identity [x1,x2][x3,x4,x5]=0. This variety is one of the several minimal varieties of exponent 3 (and all proper subvarieties are of exponents 1 and 2). We describe asymptotically its proper subvarieties. More precisely, we define certain algebras ℛ2k for any k∈ℕ and show that if [Formula: see text] is a proper subvariety of [Formula: see text], then the T-ideal of its polynomial identities is asymptotically equivalent to the T-ideal of the identities of one of the algebras [Formula: see text], E, ℛ2k or ℛ2k⊕E, for a suitable k∈ℕ. We give also another description relating the T-ideals of the proper subvarieties of [Formula: see text] with the polynomial identities of upper triangular matrices of a suitable size.