Identidades polinomiais Zn-graduadas das álgebras de matrizes

Abstract

Let F be a field and denote by Zn the group of integers modulo n. In this dissertation, we will study a description of a finite basis for the Zn-graded polynomial identities of the matrix algebra of order n over F, when n > 2. Different methods are employed according to the characteristic of the field. If the characteristic of F is zero, we will to study the paper of Vasilovsky, in which one of the main strategies is to reduce the study of the Zn- graded polynomial identities to work with multilinear polinomials. In the case where F is an infinite field of any characteristic, we will use the paper of Azevedo, focusing on the study of the multihomogeneous polynomials. This fact makes the problem more difficult, and techniques such as generic matrices are employed.