Magnifying Elements in Semigroups of Fixed Point Set Transformations Restricted by an Equivalence Relation

Abstract

Let $X$ be a nonempty set and $\rho$ be an equivalence relation on $X$ . For a nonempty subset $S$ of $X$ , we denote the semigroup of transformations restricted by an equivalence relation $\rho$ fixing $S$ pointwise by $E_{F\left(S\right)}\left(X,\rho \right)$ . In this paper, magnifying elements in $E_{F\left(S\right)}\left(X,\rho \right)$ will be investigated. Moreover, we will give the necessary and sufficient conditions for elements in $E_{F\left(S\right)}\left(X,\rho \right)$ to be right or left magnifying elements.