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

Abstract

We prove that the wreath product $C=AwrB$ 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

References in corpus (2)

• Algebras with the same (algebraic) geometry
• Algebraic geometry over algebraic structures III: Equationally Noetherian property and compactness