Oleg Gutik

activity

20082024

most citedEmbedding the bicyclic semigroup into countably compact topological semigroups

33 citations · 241 across the 65 of their papers we have counts for

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61 papers · 1 filter

math.GR2024★ 2 cited

The semigroup of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set

Oleg Gutik, Maksym Shchypel

We study algebraic properties of the semigroup $O I_{n} (L)$ of finite partial order isomorphisms of the rank $\leq n$ of an infinite linearly ordered set $(L,\leqslant…

math.GR2024

On semitopological simple inverse $ω$ -semigroups with compact maximal subgroups

Oleg Gutik, Kateryna Maksymyk

We describe the structure of ( $0$ -)simple inverse Hausdorff semitopological $ω$ -semigroups with compact maximal subgroups. In particular, we show that if $S$ is a simple inverse Ha…

math.GR2023

On the semigroup of injective monoid endomor\-phisms of the monoid $B_{ω}^{F}$ with the two-elements family $F$ of inductive nonempty subsets of $ω$

Oleg Gutik, Inna Pozdniakova

We study injective endomorphisms of the semigroup $B_{ω}^{F}$ with the two-elements family $F$ of inductive nonempty subsets of $ω$ . We describe the…

math.GR2023

On automorphisms of the semigroup $B_{ω}^{F}$ in the case when the family $F$ consists of nonempty inductive subsets of $ω$

Oleg Gutik, Mykola Mykhalenych

Let $F$ be a family of nonempty inductive subsets of $ω$ . It is proved that an injective endomorphism $ε$ of the semigroup $B_{ω}^{F}$ is t…

math.GR2023

On homomorphisms of bicyclic extensions of archimedean totally ordered groups

Oleg Gutik, Oksana Prokhorenkova

Let $B^{+} (G)$ be the bicyclic extension of a totally ordered group $G$ which is defined in [O. Gutik, D. Pagon, and K. Pavlyk, Congruences on bicyclic extensions of a line…

math.GR2022★ 2 cited

On a semitopological semigroup $B_{ω}^{F}$ when a family $F$ consists of inductive non-empty subsets of $ω$

Oleg Gutik, Mykola Mykhalenych

Let $B_{ω}^{F}$ be the bicyclic semigroup extension for the family $F$ of $ω$ -closed subsets of $ω$ which is introduced in \cite{Gutik-Mykhalenych=20…

math.GR2022★ 1 cited

On the semigroup of injective endomorphisms of the semigroup $B_{ω}^{F_{n}}$ which is generated by the family $F_{n}$ of initial finite intervals of $ω$

Oleg Gutik, Olha Popadiuk

In the paper we describe injective endomorphisms of the inverse semigroup $B_{ω}^{F}$ , which is introduced in the paper [O. Gutik and M. Mykhalenych, \emph{On…

math.GR2022★ 3 cited

On the semigroup $B_{ω}^{F_{n}}$ which is generated by the family $F_{n}$ of finite bounded intervals of $ω$

Oleg Gutik, Olha Popadiuk

We study the semigroup $B_{ω}^{F}$ , which is introduced in the paper [O. Gutik and M. Mykhalenych, \emph{On some generalization of the bicyclic monoid}, Visnyk…

math.GR2022

On the group of automorphisms of the semigroup $B_{Z}^{F}$ with the family $F$ of inductive nonempty subsets of $ω$

Oleg Gutik, Inna Pozdniakova

We study automorphisms of the semigroup $B_{Z}^{F}$ with the family $F$ of inductive nonempty subsets of $ω$ and prove that the group $\ma…

math.GR2022

On endomorphisms of the bicyclic semigroup and the extended bicyclic semigroup

Oleg Gutik, Oksana Prokhorenkova, Diana Sekh

It is proved that the semigroups $End (B_{ω})$ and $End (B_{Z})$ of the endomorphisms of the bicyclic semigroup $…

math.GR2021★ 3 cited

On a locally compact monoid of cofinite partial isometries of $N$ with adjoined zero

Oleg Gutik, Pavlo Khylynskyi

Let $C_{N}$ be a monoid which is generated by the partial shift $α : n \mapsto n + 1$ of the set of positive integers $N$ and its inverse partial shift $…

math.GR2021

On group congruences on the semigroup $B_{ω}^{F}$ and its homomorphic retracts in the case when a family $F$ consists of inductive non-empty subsets of $ω$

Oleg Gutik, Mykola Mykhalenych

We study group congruences on the semigroup $B_{ω}^{F}$ and its homomorphic retracts in the case when an $ω$ -closed family $F$ which consists of indu…

math.GR2021★ 1 cited

On the semigroup $B_{ω}^{F}$ which is generated by the family $F$ of atomic subsets of $ω$

Oleg Gutik, Oleksandra Lysetska

We study the semigroup $B_{ω}^{F}$ , which is introduced in [O. Gutik and M. Mykhalenych, \emph{On some generalization of the bicyclic monoid}, Visnyk Lviv. Uni…

math.GR2021

Polycyclic extensions of semigroups

Oleg Gutik, Pavlo Khylynskyi

In the paper we introduce a notion of the Bruck-Reilly $λ$ -polycyclic extension of a monoid $S$ with a homomorphism $θ$ which is an analogue of the Bruck-Reilly extension of a mono…

math.GR2021

On some generalization of the bicyclic monoid

Oleg Gutik, Mykola Mykhalenych

We introduce an algebraic extension $B_{ω}^{F}$ of the bicyclic monoid for an arbitrary $ω$ -closed family $F$ subsets of $ω$ which generalizes the bi…

math.GR2021★ 1 cited

On the semigroup generating by extended bicyclic semigroup and a $ω$ -closed family

Oleg Gutik, Inna Pozdnyakova

The algebraic extension $B_{Z}^{F}$ of the extended bicyclic semigroup for an arbitrary $ω$ -closed family $F$ subsets of $ω$ is introduced…

math.GR2020

On the monoid of cofinite partial isometries of $N$ with the usual metric

Oleg Gutik, Anatolii Savchuk

In the paper we show that the monoid $I N_{\infty}$ of all partial cofinite isometries of positive integers does not embed isomorphically into the monoid $\mathbf{…

math.GR2020

The monoid of monotone injective partial selfmaps of the poset $(N^{3}, ⩽)$ with cofinite domains and images

Oleg Gutik, Olha Krokhmalna

Let $n$ be a positive integer $⩾ 2$ and $N_{⩽}^{n}$ be the $n$ -th power of positive integers with the product order of the usual order on $N$ . In th…

math.GR2019

On a semitopological extended bicyclic semigroup with adjoined zero

Oleg Gutik, Kateryna Maksymyk

In the paper it is shown that every Hausdorff locally compact semigroup topology on the extended bicyclic semigroup with adjoined zero $C_{Z}^{0}$ is di…

math.GR2019

On the monoid of cofinite partial isometries of $N^{n}$ with the usual metric

Oleg Gutik, Anatolii Savchuk

In this paper we study the structure of the monoid $I N_{\infty}^{n}$ of cofinite partial isometries of the $n$ -th power of the set of positive integers $N$ …

math.GR2019

Extensions of semigroups by symmetric inverse semigroups of a bounded finite rank

Oleg Gutik, Oleksandra Sobol

We study the semigroup extension $I_{λ}^{n} (S)$ of a semigroup $S$ by symmetric inverse semigroups of a bounded finite rank. We describe idempotents and regular elements of t…

math.GR2019

The semigroup of star partial homeomorphisms of a finite deminsional Euclidean space

Oleg Gutik, Kateryna Melnyk

In the paper the notion of a star partial homeomorphism of a finite dimensional Euclidean space $R^{n}$ is introduced. We describe the structure of the semigroup $\mathbf{PS…

math.GR2019

The semigroup of monotone co-finite partial homeomorphisms of the real line

Oleg Gutik, Kateryna Melnyk

In the paper we investigate the semigroup of monotone co-finite partial homeomorphisms of the space of the usual real line $R$ . We prove that the inverse semigroup $\maths…

math.GR2019

On the semigroup $ID_{\infty}$

Oleg Gutik, Anatolii Savchuk

We study the semigroup $ID_{\infty}$ of all partial isometries of the set of integers $Z$ . It is proved that the quotient semigroup $\textbf{ID}_{\infty}/\mathfra…

The semigroup of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set

On semitopological simple inverse ω-semigroups with compact maximal subgroups

On the semigroup of injective monoid endomor\-phisms of the monoid BωF​ with the two-elements family F of inductive nonempty subsets of ω

On automorphisms of the semigroup BωF​ in the case when the family F consists of nonempty inductive subsets of ω

On homomorphisms of bicyclic extensions of archimedean totally ordered groups

On a semitopological semigroup BωF​ when a family F consists of inductive non-empty subsets of ω

On the semigroup of injective endomorphisms of the semigroup BωFn​​ which is generated by the family Fn​ of initial finite intervals of ω

On the semigroup BωFn​​ which is generated by the family Fn​ of finite bounded intervals of ω

On the group of automorphisms of the semigroup BZF​ with the family F of inductive nonempty subsets of ω

On endomorphisms of the bicyclic semigroup and the extended bicyclic semigroup

On a locally compact monoid of cofinite partial isometries of N with adjoined zero

On group congruences on the semigroup BωF​ and its homomorphic retracts in the case when a family F consists of inductive non-empty subsets of ω

On the semigroup BωF​ which is generated by the family F of atomic subsets of ω

Polycyclic extensions of semigroups

On some generalization of the bicyclic monoid

On the semigroup generating by extended bicyclic semigroup and a ω-closed family

On the monoid of cofinite partial isometries of N with the usual metric

The monoid of monotone injective partial selfmaps of the poset (N3,⩽) with cofinite domains and images

On a semitopological extended bicyclic semigroup with adjoined zero

On the monoid of cofinite partial isometries of Nn with the usual metric

Extensions of semigroups by symmetric inverse semigroups of a bounded finite rank

The semigroup of star partial homeomorphisms of a finite deminsional Euclidean space

The semigroup of monotone co-finite partial homeomorphisms of the real line

On the semigroup ID∞​

On semitopological simple inverse $ω$ -semigroups with compact maximal subgroups

On the semigroup of injective monoid endomor\-phisms of the monoid $B_{ω}^{F}$ with the two-elements family $F$ of inductive nonempty subsets of $ω$

On automorphisms of the semigroup $B_{ω}^{F}$ in the case when the family $F$ consists of nonempty inductive subsets of $ω$

On a semitopological semigroup $B_{ω}^{F}$ when a family $F$ consists of inductive non-empty subsets of $ω$

On the semigroup of injective endomorphisms of the semigroup $B_{ω}^{F_{n}}$ which is generated by the family $F_{n}$ of initial finite intervals of $ω$

On the semigroup $B_{ω}^{F_{n}}$ which is generated by the family $F_{n}$ of finite bounded intervals of $ω$

On the group of automorphisms of the semigroup $B_{Z}^{F}$ with the family $F$ of inductive nonempty subsets of $ω$

On a locally compact monoid of cofinite partial isometries of $N$ with adjoined zero

On group congruences on the semigroup $B_{ω}^{F}$ and its homomorphic retracts in the case when a family $F$ consists of inductive non-empty subsets of $ω$

On the semigroup $B_{ω}^{F}$ which is generated by the family $F$ of atomic subsets of $ω$

On the semigroup generating by extended bicyclic semigroup and a $ω$ -closed family

On the monoid of cofinite partial isometries of $N$ with the usual metric

The monoid of monotone injective partial selfmaps of the poset $(N^{3}, ⩽)$ with cofinite domains and images

On the monoid of cofinite partial isometries of $N^{n}$ with the usual metric

On the semigroup $ID_{\infty}$