Equations over direct powers of algebraic structures in relational languages

TL;DR

This paper investigates when direct powers of relational structures that approximate groups and semigroups are equationally Noetherian, providing criteria based on their algebraic properties.

Contribution

It introduces criteria for when direct powers of certain relational structures are equationally Noetherian, expanding understanding of algebraic equations in relational contexts.

Findings

Criteria established for equationally Noetherian direct powers

Conditions identified for algebraic structures approximating groups and semigroups

Advances in understanding equations over relational structures

Abstract

We study equations over relational structures that approximate groups and semigroups. For such structures we proved the criteria, when a direct power of such algebraic structures is equationally Noetherian.