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|Type:||Artigo de periódico|
|Title:||Graded identities for T-prime algebras over fields of positive characteristic|
de Azevedo, SS
|Abstract:||In this paper we study 2-graded polynomial identities. We describe bases of these identities satisfied by the matrix algebra of order two M-2(K), by the algebra M-1,M-1(G), and by the algebra G circle times(K) G. Here K is an arbitrary infinite field of characteristic not 2, G stands for the Grassmann (or exterior) algebra of an infinite dimensional vector space over K, and M-1,M-1 (G) is the algebra of all 2 x 2 matrices over G whose entries on the main diagonal are even elements of G, and those on the second diagonal axe odd elements of G. The gradings on these three algebras are supposed to be the standard ones. It turns out that the graded identities of these three algebras are closely related, and furthermore M-1,M-1 (G) and G circle times G satisfy the same 2-graded identities provided that char K = 0. When char K = p > 2, then the algebra G circle times G satisfies some additional 2-graded identities that are not identities for M-1,M-1(G). The methods used in the proofs are based on appropriate constructions for the corresponding relatively free algebras, on combinatorial properties of permutations, and on a version of Specht's commutator reduction. We hope that this paper is a step towards the description of the ordinary identities satisfied by the algebras G circle times G and M-1,M-1(G) over an infinite field of positive characteristic. Note that in characteristic 0 such a description was given in  and in .|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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