A Note on Regularity of Certain Semigroups of Transformations Preserving a Reflexive and Transitive Relation

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Published: Sep 26, 2023
Keywords:
Reflexive relation Regular element Transformation semigroup Transitive relation

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Kitsanachai Sripon
Department of Mathematics, Faculty of Science, Naresaun University, Phitsanulok 65000, Thailand
Ekkachai Laysirikul
Department of Mathematics, Faculty of Science, Naresaun University, Phitsanulok 65000, Thailand
Yanisa Chaiya
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand, Thammasat University Research Unit in Algebra and Its Applications, Thammasat University, Pathum Thani 12120, Thailand

Abstract

In this paper, we introduce semigroups of transformations that preserve a reflexive and transitive relation. These semigroups are generalizations of well-known classes of transformation semigroups, namely semigroups of transformations preserving an equivalence relation and semigroups of order-preserving transformations. Additionally, we investigate the necessary and sufficient conditions for elements within such a semigroup, in certain cases, to be regular. These results extend the existing knowledge in the aforementioned semigroups.

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How to Cite
Sripon, K., Laysirikul, E., & Chaiya, Y. (2023). A Note on Regularity of Certain Semigroups of Transformations Preserving a Reflexive and Transitive Relation. Science & Technology Asia, 28(3), 37–43. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/248936
Issue
Vol.28 No.3 (July-September 2023)
Section
Physical sciences
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References

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