The natural partial order on some transformation semigroups

Authors

  • S. Chaopraknoi Chulalongkorn University
  • T. Phongpattanacharoen
  • P. Rawiwan

Keywords:

transformation semigroup, natural partial order, left [right] compatible, minimal [maximal] elements

Abstract

For a semigroup \(S\), let \(S1\) be the semigroup obtained from \(S\) by adding a new symbol 1 as its identity if \(S\) has no identity; otherwise let \(S1=S\). Mitsch defined the natural partial order ⩽ on a semigroup \(S\) as follows: for \(a,b∈S\), \(a⩽b\) if and only if \(a=xb=by\) and \(a=ay\) for some \(x,y∈S1\). In this paper, we characterise the natural partial order on some transformation semigroups. In these partially ordered sets, we determine the compatibility of their elements, and find all minimal and maximal elements. 10.1017/S0004972713000580

Published

2014-01-27

Issue

Section

Articles