Left and Right Magnifying Elements in Certain Linear Transformation Semigroups

Pongsan Prakitsri

Abstract

An element a in a semigroup S is called a left (right) magnifying element in S if aM = S (Ma=S) for some proper subset M of S. In this paper, we determine whether or not the linear transformation semigroups with infinite nullity and co-rank have left and right magnifying elements, and provide a characterization if such elements exist.