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Magnifiers in Some Generalization of the Full 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

An element a of a semigroup S is called a left [right] magnifier if there exists a proper subset M of S such that a M = S ( M a = S ) . Let T ( X ) denote the semigroup of all transformations on a nonempty set X under the composition of functions, P = { X i ∣ i ∈ Λ } be a partition, and ρ be an equivalence relation on the set X . In this paper, we focus on the properties of magnifiers of the set T ρ ( X , P ) = { f ∈ T ( X ) ∣ ∀ ( x , y ) ∈ ρ , ( x f , y f ) ∈ ρ and X i f ⊆ X i for all i ∈ Λ } , which is a subsemigroup of T ( X ) , and provide the necessary and sufficient conditions for elements in T ρ ( X , P ) to be left or right magnifiers.

Suggested Citation

  • Thananya Kaewnoi & Montakarn Petapirak & Ronnason Chinram, 2020. "Magnifiers in Some Generalization of the Full Transformation Semigroups," Mathematics, MDPI, vol. 8(4), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:473-:d:338986
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