Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2753

Full Length Research Paper

Natural partial order on a semi group of self-E-preserving transformations

Chaiwat Namnak
  • Chaiwat Namnak
  • Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.
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Ekkachai Laysirikul
  • Ekkachai Laysirikul
  • Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.
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  •  Accepted: 21 September 2012
  •  Published: 31 January 2013

Abstract

Let T(X) denote the full transformation semigroup on a set X. For an arbitrary equivalence relation E on X, we consider a sub semi-group of T(X) defined by: TSE(X)={α∈T(X):(x,xα)∈E for each x∈X} which is called the self-E-preserving transformation semi-group on X. In this paper, we discussed a natural partial order on TSE (X) and characterize when two elements of TSE (X) are related under this order. We also described the left compatibility and right compatibility of each element of TSE (X) with respect to this order.

Key words: Natural partial order, transformation semigroup, compatible.