Wreath products of semigroups in universal algebraic geometry and Plotkin's problem

TL;DR

This paper proves that the wreath product of a semigroup with zero and an infinite cyclic semigroup is logically Noetherian, addressing a specific problem in universal algebraic geometry.

Contribution

It demonstrates that certain wreath products are $q_ au$-compact, providing a partial solution to Plotkin's problem in the context of universal algebraic geometry.

Findings

Wreath product of a semigroup with zero and an infinite cyclic semigroup is $q_ au$-compact.

The result advances understanding of algebraic properties of wreath products.

Partial resolution of Plotkin's problem regarding wreath products.

Abstract

We prove that the wreath product $C=A wr B$ of a semigroup $A$ with zero and an infinite cyclic semigroup $B$ is $q_\omega$-compact (logically Noetherian). Our result partially solves the Plotkin`s problem about wreath products