A-polynomial identities in associative algebras / A-identidades polinomiais em algebras associativas
AUTOR(ES)
Dimas Jose Gonçalves
DATA DE PUBLICAÇÃO
2009
RESUMO
In this PhD thesis we study polynomial identities in associative algebras. More precisely we study the A-ideIltities for several important classes of algebras. The first main result of the thesis gives a complete description of the A-identities for the Grassmann algebra over an algebraically closed field of characteristic O. In this way we give a positive answer to a conjecture due to Henke and Regev. Afterwards we study A-identities for the upper triangular matrix algebras. We give a lower bound for the minimal degree of an A-identity satisfied by such algebras. As a corollary we give a negative answer to another conjecture due to Henke and Regev. Furthermore we describe the A-identities of degree 5 for the upper triangular matrices of order 2 and compute the minimal degree of an A-identity for such algebras of order 3 and 4
ASSUNTO(S)
grassmann algebra polynomial identity a-polynomial identity identidade polinomial pi-algebras grassmann upper triangular matrices pi-algebra a-identidade polinomial matrizes triangulares superiores algebra de
