The goal of this undergraduate thesis is to study some introdutory concepts and results of the PI-algebras theory. In particular, as main results, we describe the polinomial identities of the Grassmann algebra and 2 x 2 ...

One of the main goals of this project is to study the index of vector fields in compact surfaces and present the Poincar´e-Hopf Theorem, remarking that such a result connects topological elements to geometric objects.

In this work, we study the concepts of degree and local degree for maps between manifolds. Furthermore, we define the Poincaré-Hopf index and study some relevant proprieties of this index such as the famous Poincaré-Hopf ...

In this work, basic definitions and results on Algebras with Polynomial Identities are introduced, some classic results of the theory that involve them are stated and demonstrated, such as the Amitsur-Levitzki Theorem, ...