Procedures are given for constructing Peirce-evanescent identities in baric algebras, with mutation algebras shown to satisfy all such identities so that any subset of the base field K can serve as the Peirce spectrum.
Crit\`ere d'existence d'idempotent bas\'e sur les alg\`ebres de R\'etrocroisement
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abstract
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.
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Identit\'es pond\'er\'ees Peirce-\'evanescentes
Procedures are given for constructing Peirce-evanescent identities in baric algebras, with mutation algebras shown to satisfy all such identities so that any subset of the base field K can serve as the Peirce spectrum.