Identidades polinomiais graduadas para álgebras de matrizes.

Abstract

The main theme of this dissertation is the description of the graded polynomial identities of the algebra Mn(K). Diferent methods are used depending on the characteristic of the field: if Char K = 0, the description of the graded identities is reduced to the description of the multilinear graded identities, what was done in Chapter 2, where the identities of Mn(K) are described for a wide class of elementary gradings; if Char K =p>0 and K is in nite, the description of the graded identities is reduced to the study of the multi-homogeneous identities, wich makes it harder, and techniques such as the construction of generic algebras are necessary. In Chapter 3 the Z and Zn-graded identities of Mn(K) are described for an infinite field K