On Magnifying Elements in E-Preserving Partial Transformation Semigroups

Let S be a semigroup. An element a of S is called a right [ left] magnifying element if there exists a proper subset M of S satisfying S = Ma [ S = aM]. Let E be an equivalence relation on a nonempty set X. In this paper, we consider the semigroup P ( X, E) consisting of all E- preserving partial transformations, which is a subsemigroup of the partial transformation semigroup P ( X). The main propose of this paper is to show the necessary and sufficient conditions for elements in P ( X, E) to be right or left magnifying.