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

作者：Mallol Cristian; Varro Richard^*

来源：Journal of Algebra, 2013, 375: 22-32.

DOI：10.1016/j.jalgebra.2012.11.019

• Baric algebras
• Gametization of algebra
• Non-homogeneous polynomial identity omega-polynomial identity

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.

• 出版日期2013-2-1