Les pol( n,m)-algèbres: identités polynômiales symétriques dans des algèbres

Abstract

Symmetric polynomial identities arise in several algebras. In this work we study nonassociative, noncommutative algebras verifying these kinds of identities. The equivalence between these algebras and algebras satisfying particular monomial relations (in which a linear form appears) is proved. We thus present simplified definitions of some classical baric algebras, for instance, Bernstein's algebras.