Estudos sobre A-identidades polinomiais

Abstract

The aim of this work is to study A-identities in associative algebras. More specifically, we study the A-identities of the tensor square of the unitary and infinite dimensional Grassmann algebra E, denoted by R, and we find the minimum degree of an A-identity of R. Due to Kemer's Tensor Product Theorem, in characteristic zero the algebras M_{1,1}(E) and R are PI-equivalent. Thus, in several moments we deal with the algebra M_{1,1}(E). In a second moment, we study the Z_2-graded A-identities of M_{1,1}(E). In this sense, we describe the set of such identities and calculate its respective graded A-codimensions.