Identidades polinomiais para a álgebra de Grassmann

Abstract

In this work, we study algebras with polynomial identities (PI-algebras), with particular emphasis on the polynomial identities of the Grassmann algebra. To this end, we develop the necessary background on algebras, free algebras, and T-ideals. In addition to the polynomial identities of the Grassmann algebra, we also present the polynomial identities of the matrix algebras M2(K) and Un(K). Furthermore, we study the T-ideal of commutative algebras and, finally, present a basis for the T-ideal of the Grassmann algebra.