On equations over direct powers of algebraic structures

TL;DR

This paper investigates the conditions under which direct powers of algebraic structures like graphs, posets, and matroids are equationally Noetherian, and shows that finite structures' powers are always weakly so.

Contribution

It provides new criteria for when direct powers of certain algebraic structures are equationally Noetherian and establishes that finite structures' powers are weakly equationally Noetherian.

Findings

Criteria for equationally Noetherian direct powers

Finite algebraic structures' powers are weakly equationally Noetherian

Advances understanding of equations over complex algebraic systems

Abstract

We study systems of equations over graphs, posets and matroids. We give the criteria, when a direct power of such algebraic structures is equationally Noetherian. Moreover we prove that any direct power of a finite algebraic structure is weakly equationally Noetherian.