http://lattes.cnpq.br/3333115830597692; CAMPOS, Suene Ferreira.
Resumo:
In this work we present a study about the behavior of polynomial identities
of tensor products of T-prime T-ideals over infinite fields of different characteristics.
More precisely, we present the Tensor Product Theorem (TPT), described by Kemer
for fields of characteristic zero, and verify its validity over infinite fields with positive
characteristic. First, based on results of Azevedo and Koshlukov, we study the Tideals
of the algebrasM1,1(G) eG⊗G, for infinite fields of characteristic zero and
characteristicp>2. Here,G=G0 ⊕G1 is the Grassmann algebra of infinite dimension
andM1,1(G) is the subalgebras ofM2(G) consisting of matrices of order2 which main
diagonal entries are inG0 and the secondary diagonal entries are inG1. Second, using
methods introduced by Regev and developed by Azevedo, Fidélis and Koshlukov, we
verify the validity of the TPT for fields of positive characteristic, when it is restricted
to multilinear polynomials. Finally, we present some results of Alves, Azevedo, Fidelis
and Koshlukov, which show that the TPT is false when the basis field is infinite and
has characteristicp>2.