On Magnifying Elements in Transformation Semigroups with a Fixed Point Set

Montakarn Petapirak, Thananya Kaewnoi, Ronnason Chinram

Abstract

An element a of a semigroup S is called a left (right) magnifying element if there is a proper subset M of S such that aM = S (Ma = S). For a fixed point set, a nonempty subset of a set X, we determine the conditions for functions in the transformation semigroups on X fixing all elements in the given fixed point set to be a left or right magnifying element as well as the existence of such elements.