Magnifying Elements in Some Subsemigroups of the Full Transformation Semigroups

Annual Meeting in Mathematics 2024

Abstract

For a semigroup S, an element a in S is called a left (right) magnifying element of S if there exists a proper subset M of S such that aM = S (Ma = S). In this paper, we provide necessary and sufficient conditions for elements in the semigroups of opposite monomorphisms and the semigroups of opposite epimorphisms on an infinite set X to be left (right) magnifying elements. We also determine some properties of magnifying elements in these semigroups.