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Research articles

ScienceAsia 39(2013): 316-318 |doi: 10.2306/scienceasia1513-1874.2013.39.316

Some subsemigroups of the full transformation semigroups

Chaiwat Namnak*, Ekkachai Laysirikul

ABSTRACT:     A nonempty subset T of a semigroup S is called a subsemigroup of S if T2T, that is, xyT for all x,yT. 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.

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Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000 Thailand

* Corresponding author, E-mail: chaiwatn@nu.ac.th

Received 13 Sep 2012, Accepted 13 Mar 2013