3 citations · 14 across the 19 of their papers we have counts for
20 papers
On equations over direct powers of algebraic structures
A. Shevlyakov
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…
Equations over direct powers of algebraic structures in relational languages
A. Shevlyakov
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 i…
Wreath products of semigroups in universal algebraic geometry and Plotkin's problem
A. Shevlyakov
We prove that the wreath product of a semigroup with zero and an infinite cyclic semigroup is -compact (logically Noetherian). Our result partially solves t…
On group automorphisms in universal algebraic geometry
Artem N. Shevlyakov
In this paper, we study group equations with occurrences of automorphisms. We describe equational domains in this class of equations. Moreover, we solve a number of open problem po…
On equations over Brandt semigroups
Mikhail Vakhrameev
In this paper, we study equations over Brandt semigroup . We compute that the number of unsolvable equations in one variable asymptotically equals , and the ave…
On irreducible algebraic sets over linearly ordered semilattices II
Artem N. Shevlyakov
Equations over linearly ordered semilattices are studied. For any equation we find irreducible components of its solution set and compute the average number of irreduci…