Action of the group of operators of gametisation on ω-polynomial identities

JOURNAL OF ALGEBRA

卷:375

Article

Mallol, Cristian¹  Varro, Richard² 

[1] Univ La Frontera, Dept Ingn Matemat, Temuco, Chile

[2] Univ Montpellier 3, Dept Math & Informat Appl, F-34199 Montpellier, France

关键词: Baric algebras;    Gametization of algebra;    Non-homogeneous polynomial identity omega-polynomial identity;   

DOI  :  10.1016/j.jalgebra.2012.11.019

来源: Elsevier

【 摘 要 】

The gametization process reduces the study of non-commutative and non-associative algebras satisfying non-homogeneous polynomial identities with variables in X = {x(1), . . . , x(n)} to algebras verifying simpler identities. However after a gametization, certain identities remain invariant and other identities, said universal invariant, are invariant for every gametization. Now in the case n = 1, for all algebras. satisfying a universal invariant polynomial identity studied until now, we know that the existence of an idempotent is not certain. Using an action of the gametization operators group on the non-commutative and non-associative algebra of polynomials K (X), we give all identities which are invariant and universal invariant by gametization. (C) 2012 Elsevier Inc. Tous droits reserves.

【 授权许可】

Free