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

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已出版: 9月 26, 2023

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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

摘要

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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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. 取读于 从 https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/248936
期
Vol.28 No.3 (July-September 2023)
栏目
Physical sciences
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参考

Howie JM. Fundamentals of Semigroup Theory, Oxford: Clarendon Press; 1995.

Pei H. Regularity and Green’s relations for semigroups of transformations that preserve an equivalence, Communications in Algebra 2005;33(1):109-18.

Kaewnoi T, Petapirak M, Chinram R.Magnifying elements in a semigroup of transformations preserving equivalence relation, Korean Journal of Mathematics 2019;27:269-77.