DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in press

Authors:

- Srisawat

Jitsapa Srisawat

Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University

email: jitsupa.sris@dome.tu.ac.th

0009-0003-4413-9231

- Chaiya

Yanisa Chaiya

Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University

email: yanisa@mathstat.sci.tu.ac.th

0000-0002-7119-2658

Title:

Semigroups of partial transformations with invariant set: Green's relations, unit regularity and directly finiteness

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Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2024-03-27 , Revised: 2024-07-11 , Accepted: 2024-07-11 , Available online: 2024-08-20 , https://doi.org/10.7151/dmgaa.1459

Abstract:

Given a nonempty set $X$, and let $P(X)$ denote the partial transformation semigroup on $X$. For a nonempty subset $Y$ of $X$, define $\overline{PT}(X,Y)$ as follows: $$\overline{PT}(X,Y)=\{\alpha\in P(X) : (\dom(\alpha)\cap Y)\alpha\subseteq Y\}.$$ Then $\pt$ is a generalization of $P(X)$, consisting of all partial transformations on $X$ that leave $Y$ as an invariant set. In this paper, we investigate the Green's relations and explore all unit regular elements. Additionally, we determine the necessary and sufficient conditions for $\pt$ to be unit regular and directly finite.

Keywords:

partial transformation semigroups, Green's relations, unit regular semigroups, directly finite semigroups

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