Magnifying elements in a semigroup of transformations preserving equivalence relation

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.