Identidades polinomiais da álgebra de Grassmann em característica positiva

Abstract

This dissertation was written with the intent of containing its main prerequisites. So, initially, we will recall some basic deĄnitions and some results from classical algebra. Then we will list some classical results of the theory of PI-algebras as well as the ones about codimensions and Hilbert series. The latter will give us tools to describe, at least partially, the polynomial identities of the Grassmann algebra in positive characteristic (mainly the unitary Grassmann algebra). Nevertheless, many of the results may work in characteristic zero too. We will take in consideration two cases: in the Ąrst one the ground Ąeld will be considered inĄnite (according to a paper written by Giambruno and Koshlukov) while in the second one we will consider the ground Ąeld to be Ąnite (according to a paper written by Regev).