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Left (Right) Regular Elements of Some Transformation Semigroups

Author

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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)

  • Worachead Sommanee

    (Department of Mathematics and Statistics, Faculty of Science and Technology, Chiang Mai Rajabhat University, Chiang Mai 50300, Thailand)

Abstract

For a nonempty set X , let T ( X ) be the total transformation semigroup on X . In this paper, we consider the subsemigroups of T ( X ) which are defined by T ( X , Y ) = { α ∈ T ( X ) : X α ⊆ Y } and S ( X , Y ) = { α ∈ T ( X ) : Y α ⊆ Y } where Y is a non-empty subset of X . We characterize the left regular and right regular elements of both T ( X , Y ) and S ( X , Y ) . Moreover, necessary and sufficient conditions for T ( X , Y ) and S ( X , Y ) to be left regular and right regular are given. These results are then applied to determine the numbers of left and right regular elements in T ( X , Y ) for a finite set X .

Suggested Citation

  • Kitsanachai Sripon & Ekkachai Laysirikul & Worachead Sommanee, 2023. "Left (Right) Regular Elements of Some Transformation Semigroups," Mathematics, MDPI, vol. 11(10), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2230-:d:1143390
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    References listed on IDEAS

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    1. Jintana Sanwong & Worachead Sommanee, 2008. "Regularity and Green's Relations on a Semigroup of Transformations with Restricted Range," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2008, pages 1-11, November.
    2. Nenthein, S., Youngkhong, P. & Kemprasit, Y., 2005. "Regular elements of some transformation semigroups," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 16(3), pages 307-314.
    3. Thananya Kaewnoi & Montakarn Petapirak & Ronnason Chinram, 2018. "On Magnifying Elements in E-Preserving Partial Transformation Semigroups," Mathematics, MDPI, vol. 6(9), pages 1-7, September.
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    Cited by:

    1. Irina Cristea & Hashem Bordbar, 2023. "Preface to the Special Issue “Algebraic Structures and Graph Theory”," Mathematics, MDPI, vol. 11(15), pages 1-4, July.

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