arXiv subjects

Dmitry V. Skokov

Publications and source records attributed to Dmitry V. Skokov.

4 recordsLinked to original sources

arXiv2025

Modular elements of the lattices of varieties of semigroups and epigroups. I

This paper is the first part of a study devoted to description of modular elements in the lattices of semigroup and epigroup varieties. We provide strengthened necessary and sufficient conditions under which a semigroup or epigroup variety constitutes a modular element in its respective lattice. These results refine previously known criteria and lay the groundwork for a complete classification, to be presented in the second part of the study.

math.GR↗

arXiv2018

Cancellable elements of the lattice of epigroup varieties

We completely determine all commutative epigroup varieties that are cancellable elements of the lattice EPI of all epigroup varieties. In particular, we verify that a commutative epigroup variety is a cancellable element of the lattice EPI if and only if it is a modular element of this lattice.

math.GR↗

arXiv2017

On modular and cancellable elements of the lattice of semigroup varieties

We completely determine all semigroup varieties satysfiyng a permutational identity of length 3 that are modular elements of the lattice of all semigroup varieties. Using this result, we provide an example of a semigroup variety that is a modular but not cancellable element of this lattice.

math.GR↗

arXiv2017

Cancellable elements of the lattice of semigroup varieties

We completely determine all commutative semigroup varieties that are cancellable elements of the lattice SEM of all semigroup varieties. In particular, we prove that, for commutative varieties, the properties of being cancellable and modular elements of SEM are equivalent.

math.GR↗