Grafos eulerianos e identidades polinomiais na álgebra Mn(K)

• Autor(a) principal: Gonçalves, Fernanda Scabio
• Data de Publicação: 2013
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/5894
• topic: Álgebra; Identidades polinomiais; Matrizes (Matemática); Grafos eulerianos; Polynomial identities; Matrix algebra; Eulerian graphs; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work we present some applications of graph theory in problems involving polynomial identities for the algebra Mn (K). A brief presentation of PI-theory and some concepts of graph theory, such as the definition of Eulerian graphs, which are the basic elements of this work, were presented to make the text self- contained. We show two different proofs of the Amitsur-Levitzki theorem, the proof of Razmyslov and other due to Swan's theorem - an important result on Eulerian graphs. Finally, a similar result of the Amitsur-Levitzki's theorem for skew-symmetric matrices is proved using elements of graph theory. We emphasize that the understanding of the technique makes it possible to simplify many results and has been an important tool in the study of PI-algebras.