A Note on Coregular Elements in Certain Semigroups of Transformations

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Published: Apr 29, 2024
DOI: https://doi.org/10.60101/past.2024.252662
Keywords:
Partial Pransformation Semigroups Regular Elements Coregular Elements

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Jitsupa Srisawat
Department of Mathematics and Statistics, Faculty of Science and Technology Thammasat University
Yanisa Chaiya
Department of Mathematics and Statistics, Faculty of Science and Technology Thammasat University

Abstract

For a non-empty set X, let P(X)  represent the partial transformation semigroup on X. For a non-empty subset Y of X, define gif.latex?{\small\overline{PT}(X,Y)}  as the semigroup 


gif.latex?\overline{PT}(X,Y)=\{\alpha\in&space;P(X)&space;:(\operatorname{dom}\alpha\cap&space;Y)\alpha\subseteq&space;Y&space;\}.


Then gif.latex?{\small\overline{PT}(X,Y)}  is a generalization of P(X) , encompassing all partial transformations on  that maintain Y as an invariant set. This paper delves into exploring the characterization of coregular elements within gif.latex?{\small\overline{PT}(X,Y)} and applies the results to obtain a similar characterization in relevant semigroups.

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How to Cite
1.
Srisawat J, Chaiya Y. A Note on Coregular Elements in Certain Semigroups of Transformations. Prog Appl Sci Tech. [Internet]. 2024 Apr. 29 [cited 2024 Jul. 3];14(1):87-90. Available from: https://ph02.tci-thaijo.org/index.php/past/article/view/252662
Issue
Vol. 14 No. 1 (2024): January - April 2024
Section
Mathematics and Applied Statistics
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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References

Chinram R, Baupradit S, Yaqoob N, Petchkaew P. Left and right magnifying elements in some generalized partial transformation semigroups. Commun. Algebra. 2021;49(7):3176-91.

Clifford AH, Preston GB. The algebraic theory of semigroups. vol. 1. Mathematical surveys. 1961.

Clifford AH, Preston GB. The algebraic theory of semigroups. vol. 2. Mathematical surveys. 1967.

Howie JM. Fundamentals of semigroup theory. Oxford university press. 1995.

Pantarak T, Chaiya Y. Regularity on semigroups of partial transformations with invariant set. Diss. Thammasat University. 2022.

Phongchan S. Rank and regularity of semigroups of transformations with invariant sets. Doctor of philosophy's thesis. Chiang Mai University. 2022.

Pantarak T, Chaiya Y. Regularity and abundance on semigroups of partial transformations with invariant set. Open Mathematics. 2023;21(1):1-12.

Bijev G, Todorov K. Coregular semigroups. Notes on Semigroups VI. Budapest. 1980;1–11.