Identidades graduadas para algebras de matrizes
AUTOR(ES)
Sergio Sardinha de Azevedo
DATA DE PUBLICAÇÃO
2003
RESUMO
The study of graded polynomial identities was motivated by its many applications to Polynomial Identities Theory, like the structure theory developed by A. Kemer. Afterwards it has become an independent object of study. The graded identities can give us interesting information about the ordinary identities. At first working with matrices of order n over infinite fields, we have found bases for the graded identities of this algebra considering Zn-grading and Z-grading. We have also proved that, up to isomorphism, there exist two non-trivial Z2-gradings for the algebra of the matrices 2×2 over a finite field of characteristic different from 2. Besides, these gradings can be recognized through graded identities. Finally, we have found bases for the Z2-graded identities of the algebras M1,1(E) and E E over an infinite field of characteristic different from 2. As a corollary, we have obtained a rather elementary proof for a theorem of Kemer, namely the algebras M1,1(E) and E E are PI equivalent.
ASSUNTO(S)
ideais (algebra) corpos finitos (algebra) aneis polinominais matrizes (matematica) aneis (algebra) algebra não-comutativa
