Identidades de álgebras de matrizes e teorema de Amitsur-Levitzki.

Abstract

In this work we approach polinomial identities of the algebra of matrix Mn(K), whereK isafield. Initially, we present the Rosset’s and Swan’s proofs for the Theorem of Amitsur-Levitzki. Afterward, we make a study on the identities of Mn(K) of2n+1 degree (considering charK =0). We end this approach with the presentation of the minimality of a integer positive number m such that the Capelli double polinomial Dm is an identity of Mn(K).