Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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MAGNIFYING ELEMENTS IN A SEMIGROUP OF TRANSFORMATIONS PRESERVING EQUIVALENCE RELATION

  • Kaewnoi, Thananya (Department of Mathematics and Statistics Prince of Songkla University) ;
  • Petapirak, Montakarn (Algebra and Applications Research Unit Department of Mathematics and Statistics Prince of Songkla University) ;
  • Chinram, Ronnason (Algebra and Applications Research Unit Department of Mathematics and Statistics Prince of Songkla University)
  • Received : 2018.05.24
  • Accepted : 2019.05.12
  • Published : 2019.06.30
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Abstract

Let X be a nonempty set, ${\rho}$ be an equivalence on X, T(X) be the semigroup of all transformations from X into itself, and $T_{\rho}(X)=\{f{\in}T(X)|(x,y){\in}{\rho}{\text{ implies }}((x)f,\;(y)f){\in}{\rho}\}$. In this paper, we investigate some necessary and sufficient conditions for elements in $T_{\rho}(X)$ to be left or right magnifying.

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References

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