Uma breve introdução à Teoria das PI-álgebras - Luccas, Luis Felipe dos Santos (Universidade Federal de São Carlos, 2023)
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 upper triangular matrix algebra when the field is infinite, we study the Amitsur-Levitzki Theorem about identities on the matrix algebra, and Regev's Theorems about the codimension and the tensor product of two PI-algebras.
A brief introduction to the theory of PI-algebras
Keywords: PI-álgebra; Álgebra de Grassmann; Matrizes triangulares superiores; Teorema de Amitsur-Levitzki; Teorema da codimensão de Regev; PI-algebra; Grassmann algebra; Upper triangular matrices; Amitsur-Levitzki Theorem; Codimension Theorem of Regev; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA