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

Authors

  • 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

Keywords:

Reflexive relation, Regular element, Transformation semigroup, Transitive relation

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.

References

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.

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Published

2023-09-26

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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