The natural partial order on the semigroup of all transformations of a set that reflect an equivalence relation

Authors

  • L. Sun
  • X. Xin

Keywords:

transformation semigroup, natural partial order, compatibility, maximal(minimal) elements

Abstract

Let ${\cal T}_X$ be the full transformation semigroup on a set $X$ and $E$ be a non-trivial equivalence relation on $X$. Denote T(X)={fTX:x,yX,(f(x),f(y))E(x,y)E}, then $T_\exists (X) $ is a subsemigroup of ${\cal T}_ X $. In this paper, we endow $T_\exists (X)$ with the natural partial order and investigate when two elements are related, then find elements which are compatible. Also, we characterize the maximal elements and the minimal elements. 10.1017/S0004972712001013

Published

2013-09-27

Issue

Section

Articles