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Invertible algebras satisfying associative identities with functional variables

Yu. Movsisyan

Yerevan State University, 1 Alex Manoogian, Yerevan 0025, Armenia

E-mail Address: movsisyan@ysu.am

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and

A. Gevorgyan

Yerevan State University, 1 Alex Manoogian, Yerevan 0025, Armenia

E-mail Address: albert.gevorgyan@ysumail.am

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https://doi.org/10.1142/S1793557120501557Cited by:1 (Source: Crossref)

Abstract

In this paper, the Belousov theorem on linearity of invertible algebras with the Schauffler $\forall \exists (\forall)$ $\forall \exists (\forall)$ -identity is extended over the other $\forall \exists (\forall)$ $\forall \exists (\forall)$ -identities of associativity. As a consequence, we obtain the equivalency of the considered $\forall \exists (\forall)$ $\forall \exists (\forall)$ -identities of associativity and nontrivial hyperidentities of associativity in systems of groups. For the considered formulas, we prove the Schauffler-type theorems, too.

Communicated by K. Denecke

Keywords:

AMSC: 03C05, 03C85, 20N05

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