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

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.