A DIVISION THEOREM FOR THE PSEUDOVARIETY GENERATED BY SEMIGROUPS OF ORIENTATION PRESERVING TRANSFORMATIONS ON A FINITE CHAIN

Abstract

In this paper we present a division theorem for the pseudovariety of semigroups OP generated by all semigroups of orientation preserving full transformations on a finite chain, which is achieved by using a natural representation of a certain monoid of transformations of a set X as a monoid of transformations of a subset of X.

Keywords:

• Semigroups of transformations
• Pseudovarieties

ACKNOWLEDGMENTS

The author wishes to thank Professors Gracinda M. S. Gomes and Jean-Eric Pin for their help in preparing this paper. This research was prepared within the project PRAXIS/2/2.1/MAT/73/94, CAUL, and it was supported, in part, by INVOTAN Grant 9/A/96/PO.