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 volume

Authors:

R. Wijarajak

Rattiya Wijarajak

Department of Mathematics and Statistics
Faculty of Science and Technology
Thammasat University (Rangsit Campus)
Pathum Thani, 12120, Thailand

email: rattiya.wija@dome.tu.ac.th

Y. Chaiya

Yanisa Chaiya

Department of Mathematics and Statistics
Faculty of Science and Technology
Thammasat University (Rangsit Campus)
Pathum Thani, 12120, Thailand

email: yanisa@mathstatsci.tu.ac.th

Title:

A Note on the Abundance of Partial Transformation Semigroups with Fixed Point Sets

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Source:

Discussiones Mathematicae - General Algebra and Applications 43(2) (2023) 241-247

Received: 2021-10-22 , Revised: 2022-03-07 , Accepted: 2022-03-07 , Available online: 2023-05-11 , https://doi.org/10.7151/dmgaa.1438

Abstract:

Given a non-empty set $X$ and let $P(X)$ be the partial transformation semigroup on $X$. For a fixed non-empty subset $Y$ of $X$, let $$ PFix(X,Y)=\{\alpha\in P(X):y\alpha=y \textrm{ for all } y\in Y\}. $$ Then $PFix(X,Y)$ is a subsemigroup of $P(X)$. In this paper, we show that $PFix(X,Y)$ is always abundant, even if it is not regular. Moreover, unit regular and coregular elements of such semigroup are all completely characterized.

Keywords:

partial transformation semigroup, abundance, unit regularity, coregularity

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