Sistema de identidades polinomiais sem base finita
AUTOR(ES)
Marcos Mesquita Resende
DATA DE PUBLICAÇÃO
2009
RESUMO
Let F be a field and let A be the free associative F-algebra (without 1) on free generators x1; x2; Let f = (x1;; xn) A and let G be an associative algebra over F. We say that f = 0 is a polynomial identity (or an identity) in G if f(g1; ; gn) = 0 for all g1; ; gn G. Two systems of polynomial identities {ui = 0}| i I} and {vj = 0} | j J} are equivalent if every associative F-algebra satisfying all the identities ui = 0 satisfies all the identities vj = 0 and vice versa. If a system of polynomial identities {ui = 0}| i I} is equivalent to some finite system of identities, we say that the system {ui = 0}| i I} has a finite basis or is finitely based. In this dissertation, we study in detail two systems of polynomial identites that are not finitely based, that is, they are not equivalent to a finite set of identities. The first one consists of a system of polynomial identities that has no finite basis in associative algebras (over a field of characteristic 2) with or without unity, whereas the second one works only in non-unitary associative algebras (over a field of characteristic 2) and contains the identity x6 = 0. This dissertation was based on the articles [7] and [8] by Gupta and Krasilnikov, and the chapter 3 from the book Free Algebras and PI-Algebras by Drensky [4].
ASSUNTO(S)
identidades polimiais matematica polynomial identities finite basis property varieties of algebras variedades de álgebra propriedade da base finita.
