Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/78570
Type: Artigo de periódico
Title: Tensor product theorems in positive characteristic
Author: Azevedo, SS
Fidelis, M
Koshlukov, P
Abstract: In this paper we study tensor products of T-prime T-ideals over infinite fields. The behaviour of these tensor products over a field of characteristic 0 was described by Kemer. First we show, using methods due to Regev, that such a description holds if one restricts oneself to multilinear polynomials only. Second, applying graded polynomial identities, we prove that the tensor product theorem fails for the T-ideals of the algebras M-1,M-1 (E) and E circle times E where E is the infinite-dimensional Grassmann algebra; M-1.1(E) consists of the 2 x 2 matrices over E having even (i.e., central) elements of E, and the other diagonal consisting of odd (anticommuting) elements of E. Note that these proofs do not depend on the structure theory of T-ideals but are 'elementary' ones. All this comes to show once more that the structure theory of T-ideals is essentially about the multilinear polynomial identities. (C) 2004 Elsevier Inc. All rights reserved.
Subject: T-prime T-ideal
variety of algebras
polynomial identities
graded identities
Country: EUA
Editor: Academic Press Inc Elsevier Science
Rights: fechado
Identifier DOI: 10.1016/j.jalgebra.2004.01.004
Date Issue: 2004
Appears in Collections:Unicamp - Artigos e Outros Documentos

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