Some subsemigroups of the full transformation semigroups
Chaiwat Namnak, Ekkachai Laysirikul · ScienceAsia · 2013
A nonempty subset T of a semigroup S is called a subsemigroup of S if T 2 ⊆ T , that is, xy ∈ T for all x, y ∈ T .For a nonempty set X, let T (X) be the semigroup of the full transformations on X, which consists of all functions from X into X with composition as the semigroup operation.The purpose of this paper is to define various subsemigroups of T (X).Necessary and sufficient conditions are given for these subsemigroups of T (X) to be equal.