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Gametization of weighted algebras. (Gamétisation d’algèbres pondérées.) (French) Zbl 1134.17312
Summary: The authors introduce the notion of gametization of a baric (weighted) algebra as a simple tool that allows to study structures that fulfil the $$\omega$$-polynomial identities. For train-identities of arbitrary order they establish the existence of invariant identities by gametization and their form is made precise. Classification results are given here for algebras of order $$\leq 4$$.

##### MSC:
 17D92 Genetic algebras 17A30 Nonassociative algebras satisfying other identities
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##### References:
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