Korean J. Math. Vol. 27 No. 2 (2019) pp.269-277
DOI: https://doi.org/10.11568/kjm.2019.27.2.269

Magnifying elements in a semigroup of transformations preserving equivalence relation

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Published: Jun 30, 2019
Keywords:
transformation semigroups, magnifying elements, equivalence relations.
Mathematics Subject Classification:
20M10, 20M20

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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

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 $T_{\rho}(X) = \{f \in T(X) \mid (x,y) \in \rho$ 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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