arXiv subjects
Publications and source records attributed to A. Shevlyakov.
We prove that the wreath product $C=A wr B$ of a semigroup $A$ with zero and an infinite cyclic semigroup $B$ is $q_ω$-compact (logically Noetherian). Our result partially solves the Plotkin`s problem about wreath products
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.
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.
Lectures notes in universal algebraic geometry for beginners