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On Magnifying Elements in E-Preserving Partial Transformation Semigroups

Author

Listed:
  • Thananya Kaewnoi

    (Department of Mathematics and Statistics, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand)

  • Montakarn Petapirak

    (Algebra and Applications Research Unit, Department of Mathematics and Statistics, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand)

  • Ronnason Chinram

    (Algebra and Applications Research Unit, Department of Mathematics and Statistics, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand
    Centre of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, Thailand)

Abstract

Let S be a semigroup. An element a of S is called a right [left] magnifying element if there exists a proper subset M of S satisfying S = M a [ S = a M ] . Let E be an equivalence relation on a nonempty set X . In this paper, we consider the semigroup P ( X , E ) consisting of all E -preserving partial transformations, which is a subsemigroup of the partial transformation semigroup P ( X ) . The main propose of this paper is to show the necessary and sufficient conditions for elements in P ( X , E ) to be right or left magnifying.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:9:p:160-:d:168254
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    Cited by:

    1. Kitsanachai Sripon & Ekkachai Laysirikul & Worachead Sommanee, 2023. "Left (Right) Regular Elements of Some Transformation Semigroups," Mathematics, MDPI, vol. 11(10), pages 1-12, May.

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