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|Type:||Artigo de periódico|
|Title:||Graded identities and PI equivalence of algebras in positive characteristic|
|Abstract:||The algebras M-a,M-b(E) &OTIMES; 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) &OTIMES; E and M-2 (E) when the base field is infinite and of characteristic p > 2. The algebra M-a,M-a(E) &OTIMES; 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 &OTIMES; E are not PI equivalent in positive characteristic, while they do satisfy the same multilinear identities.|
|Editor:||Taylor & Francis Inc|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
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