On magnifying elements in semigroups of transformations restricted by an equivalence relation with a restricted range
Thananya Kaewnoi, Phoschanun Ratanaburee, Ronnason Chinram, Montakarn Petapirak · ScienceAsia · 2023
An element a of a semigroup S is called a right (left) magnifying element if S contains a proper subset M such that M a = S (aM = S).Let Y be a nonempty subset of a set X and ρ be an equivalence relation on X .Denote the semigroup of transformations restricted by an equivalence relation with a restricted range by E(X , Y, ρ).In this paper, we investigate magnifying elements in E(X , Y, ρ) and give the necessary and sufficient conditions for elements in E(X , Y, ρ) to be a right or a left magnifying element.