Critère d’existence d’idempotent basé sur les algèbres de Rétrocroisement

ABSTRACT

We study the relationship of backcrossing algebras with mutation algebras and algebras satisfying ω-polynomial identities: we show that in a backcrossing algebra every element of weight 1 generates a mutation algebra and that for any polynomial identity f there is a backcrossing algebra satisfying f. We give a criterion for the existence of idempotent in the case of baric algebras satisfying a nonhomogeneous polynomial identity and containing a backcrossing subalgebra. We give numerous genetic interpretations of the algebraic results.

KEYWORDS:

• ω-polynomial identities
• backcrossing algebras
• baric algebras
• idempotent element
• mutation algebras

2008 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 17D92
• Secondary: 92A10