PI-Algebras
AUTOR(ES)
Alcindo Teles Galvão
DATA DE PUBLICAÇÃO
2003
RESUMO
This dissertation introduces the first notions of the combinatorial study of the theory of algebras that satisfy polynomial identities (the so-called P I -algebras), as well as some of their most important results. We present the theorems due to Kaplansky and Regev, about the tensor product of P 1-algebras. Besides, we describe some results due to Amitsur and the theorem about minimum identities in matricial algebras known as Amitsur and Levitzki s theorem. We also consider central polynomials and Posner s theorem, and Shirshov s height theorem, including Kurosh s problem. At the end of the dissertation we develop the methods discovered by Razmyslov which led him to the description of a basis for the polynomial identities satisfied by the Lie algebra of the traceless matrices of order two and, afterwards, for the (associative) algebra of all second arder matrices
ASSUNTO(S)
ideais (algebra) aneis (algebra) algebra não-comutativa
