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Existence criterion of idempotent based on backcrossing algebras. (Critère d’existence d’idempotent basé sur les algèbres de Rétrocroisement.) (French. English summary) Zbl 1427.17048

Summary: We study the relationship of backcrossing algebras with mutation algebras and algebras satisfying \(\omega\)-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.

MSC:

17D92 Genetic algebras
92D10 Genetics and epigenetics
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