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|Type:||Artigo de periódico|
|Title:||Polynomial identities of algebras in positive characteristic|
|Abstract:||The verbally prime algebras are well understood in characteristic 0 while over a field of positive characteristic p > 2 little is known about them. In previous papers we discussed some sharp differences between these two cases for the characteristic, and we showed that the so-called Tensor Product Theorem is in part no Ion-er valid in the second case. In this paper we study the Gelfand-Kirillov dimension of the relatively free algebras of verbally prime and related algebras. We compute the GK dimensions of several algebras and thus obtain a new proof of the fact that the algebras M-1,M-1 (E) and E circle times E are not PI equivalent in characteristic p > 2. Furthermore we show that the following algebras are not PI equivalent in positive characteristic: M-a,M-b(E) circle times E and Ma+b(E); M-a,M-b(E) circle times E and M-c,M-d(E) circle times E when a + b = c + d, a >= b, c >= d and a not equal c;, and finally, M-1,M-1 (E) circle times M-1,M-1 (E) and M-2,M-2(E). Here E stands for the infinite-dimensional Grassmann algebra with 1, and M-a,M-b(E) is the subalgebra Of Ma+b(E) of the block matrices with blocks a x a and b x b on the main diagonal with entries from E-0, and off-diagonal entries from E-1; E = E-0 circle times E-1 is the natural grading on E. (c) 2006 Elsevier Inc. All rights reserved.|
verbally prime algebra
|Editor:||Academic Press Inc Elsevier Science|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
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