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Type: Artigo de periódico
Title: Graded identities and PI equivalence of algebras in positive characteristic
Author: Azevedo, SS
Fidelis, M
Koshlukov, P
Abstract: The algebras M-a,M-b(E) ⊗ E and Ma+b(E) are PI equivalent over a field of characteristic 0 where E is the infinite-dimensional Grassmann algebra. This result is a part of the well-known tensor product theorem. It was first proved by Kemer in 1984-1987 (see Kemer, 1991); other proofs of it were given by Regev (1990), and in several particular cases, by Di Vincenzo (1992), and by the authors (2004). Using graded polynomial identities, we obtain a new elementary proof of this fact and show that it fails for the T-ideals of the algebras M-1,M-1 (E) ⊗ E and M-2 (E) when the base field is infinite and of characteristic p > 2. The algebra M-a,M-a(E) ⊗ E satisfies certain graded identities that are not satisfied by M-2a (E). In another paper we proved that the algebras M-1,M-1 (E) and E ⊗ E are not PI equivalent in positive characteristic, while they do satisfy the same multilinear identities.
Subject: graded identities
polynomial identities
T-prime T-ideal
Country: EUA
Editor: Taylor & Francis Inc
Citation: Communications In Algebra. Taylor & Francis Inc, v. 33, n. 4, n. 1011, n. 1022, 2005.
Rights: fechado
Identifier DOI: 10.1081/AGB-200053801
Date Issue: 2005
Appears in Collections:Unicamp - Artigos e Outros Documentos

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