Volodymyr Gavrylkiv

activity

20082026

most citedRight-topological semigroup operations on inclusion hyperspaces

19 citations · 62 across the 15 of their papers we have counts for

collaborators

20 papers

math.GR2026

On certain classes of commutative g-dimonoids

Volodymyr Gavrylkiv, Inna Hlushak, Kateryna Koporkh +2

We study g-dimonoids, which are algebraic structures equipped with two associative binary operations satisfying a prescribed system of axioms. We develop a construction of g-dimono…

math.GR2026

On the number of $g$ -dimonoids of small order

Volodymyr M. Gavrylkiv

We study $g$ -dimonoids, that is, algebraic structures endowed with two associative binary operations satisfying a specified system of axioms. The paper investigates duality and iso…

math.GR2026

On dimonoids of small order

Volodymyr M. Gavrylkiv

This paper is devoted to the study of dimonoids, i.e., algebraic structures equipped with two associative binary operations satisfying a given system of axioms. We introduce severa…

math.GR2026

Note on the number of doppelsemigroups of small order

Volodymyr M. Gavrylkiv

We study doppelsemigroups, i.e., algebraic structures equip\-ped with two associative binary operations satisfying a specified system of axioms. We investigate duality and isomorph…

math.GR2025

On some classes of noncommutative dimonoids

Volodymyr Gavrylkiv

The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the p…

math.GR2020★ 2 cited

Interassociativity and three-element doppelsemigroups

Volodymyr Gavrylkiv, Diana Rendziak

In the paper we characterize all interassociates of some non-inverse semigroups and describe up to isomorphism all three-element (strong) doppelsemigroups and their automorphism gr…

math.GR2019

Automorphism groups of superextensions of finite monogenic semigroups

Taras Banakh, Volodymyr Gavrylkiv

A family $L$ of subsets of a set $X$ is called linked if $A \cap B \neq = \emptyset$ for any $A, B \in L$ . A linked family $M$ of subsets of $X$ is maximal linked…

math.GR2018

Automorphism groups of superextensions of groups

Taras Banakh, Volodymyr Gavrylkiv

The superextension $λ (X)$ of a set $X$ consists of all maximal linked families on $X$ . Any associative binary operation $* : X \times X \to X$ can be extended to an associative binar…

math.CO2017

Difference bases in dihedral groups

Taras Banakh, Volodymyr Gavrylkiv

A subset $B$ of a group $G$ is called a difference basis of $G$ if each element $g \in G$ can be written as the difference $g = a b^{- 1}$ of some elements $a, b \in B$ . The smallest card…

math.CO2017

Difference bases in finite Abelian groups

Taras Banakh, Volodymyr Gavrylkiv

A subset $B$ of a group $G$ is called a difference basis of $G$ if each element $g \in G$ can be written as the difference $g = a b^{- 1}$ of some elements $a, b \in B$ . The smallest card…

math.CO2017★ 5 cited

Difference bases in cyclic groups

Taras Banakh, Volodymyr Gavrylkiv

A subset $B$ of an Abelian group $G$ is called a difference basis of $G$ if each element $g \in G$ can be written as the difference $g = a - b$ of some elements $a, b \in B$ . The smallest…

math.GR2013

Characterizing semigroups $X$ with commutative extensions $φ (X)$ , $λ (X)$ , $N_{2} (X)$ , $υ (X)$

Taras Banakh, Volodymyr Gavrylkiv

We characterize semigroups $X$ whose semigroups of filters $φ (X)$ , maximal linked systems $λ (X)$ , linked upfamilies $N_{2} (X)$ , and upfamilies $υ (X)$ are commutative.

math.GR2011★ 4 cited

Algebra in superextensions of inverse semigroups

Taras Banakh, Volodymyr Gavrylkiv

We find necessary and sufficient conditions on an (inverse) semigroup $X$ under which its semigroups of maximal linked systems $λ (X)$ , filters $ϕ (X)$ , linked upfamilies $N_{2} (X)$ , a…

math.GR2010★ 9 cited

Algebra in the superextensions of semilattices

Taras Banakh, Volodymyr Gavrylkiv

Given a semilattice $X$ we study the algebraic properties of the semigroup $υ (X)$ of upfamilies on $X$ . The semigroup $υ (X)$ contains the Stone-Cech extension $β (X)$ ,…

math.CT2010

Extending binary operations to funtor-spaces

Taras Banakh, Volodymyr Gavrylkiv

Given a continuous monadic functor T in the category of Tychonov spaces for each discrete topological semigroup X we extend the semigroup operation of X to a right-topological semi…

math.GR2008

Algebra in superextensions of twinic groups

Taras Banakh, Volodymyr Gavrylkiv

Given a group $X$ we study the algebraic structure of the compact right-topological semigroup $λ (X)$ consisting of maximal linked systems on $X$ . This semigroup contains the semigr…

math.GN2008

Algebra in the superextensions of groups: minimal left ideals

Taras Banakh, Volodymyr Gavrylkiv

We prove that the minimal left ideals of the superextension $λ (Z)$ of the discrete group $Z$ of integers are metrizable topological semigroups, topologically isomorphic to minimal…

math.GN2008★ 19 cited

Right-topological semigroup operations on inclusion hyperspaces

Volodymyr Gavrylkiv

We show that for any discrete semigroup $X$ the semigroup operation can be extended to a right-topological semigroup operation on the space $G (X)$ of inclusion hyperspaces on $X$ .…

math.GN2008★ 15 cited

Algebra in superextension of groups, II: cancelativity and centers

Taras Banakh, Volodymyr Gavrylkiv

Given a countable group $X$ we study the algebraic structure of its superextension $λ (X)$ . This is a right-topological semigroup consisting of all maximal linked systems on $X$ end…

math.GN2008★ 8 cited

Algebra in superextensions of groups, I: zeros and commutativity

T. Banakh, V. Gavrylkiv, O. Nykyforchyn

Given a group $X$ we study the algebraic structure of its superextension $λ (X)$ . This is a right-topological semigroup consisting of all maximal linked systems on $X$ endowed with…

On certain classes of commutative g-dimonoids

On the number of g-dimonoids of small order

On dimonoids of small order

Note on the number of doppelsemigroups of small order

On some classes of noncommutative dimonoids

Interassociativity and three-element doppelsemigroups

Automorphism groups of superextensions of finite monogenic semigroups

Automorphism groups of superextensions of groups

Difference bases in dihedral groups

Difference bases in finite Abelian groups

Difference bases in cyclic groups

Characterizing semigroups X with commutative extensions φ(X), λ(X), N2​(X), υ(X)

Algebra in superextensions of inverse semigroups

Algebra in the superextensions of semilattices

Extending binary operations to funtor-spaces

Algebra in superextensions of twinic groups

Algebra in the superextensions of groups: minimal left ideals

Right-topological semigroup operations on inclusion hyperspaces

Algebra in superextension of groups, II: cancelativity and centers

Algebra in superextensions of groups, I: zeros and commutativity

On the number of $g$ -dimonoids of small order

Characterizing semigroups $X$ with commutative extensions $φ (X)$ , $λ (X)$ , $N_{2} (X)$ , $υ (X)$