Minimal Varieties and Identities of Relatively Free Algebras

Abstract

Let K be a field of characteristic zero and let 5 be the variety of associative algebras over K, defined by the identity x 1 x 2 x 3 x 4 x 5 . It is well-known that such variety is a minimal variety and that it is generated by the algebrawhere E = E 0 ⊕ E 1 is the Grassmann algebra. In this article, for any positive integer k, we describe the polynomial identities of the relatively free algebras of rank k of 5 ,