Absolute flatness of regular semigroups with a finite height function

Abstract

In this paper we give a sufficient condition for regular semigroups with a finite height function to be left absolutely flat. As a consequence, we can show that the semigroup Λ(S) of all right translations of a primitive regular semigroupS with only finitely manyR-classes, with composition being from left to right, is absolutely flat and give a generalization of a Bulman-Fleming and McDowell result concerning absolutely flat semigroups from primitive regular semigroups to regular semigroups with a finite height function. These results give examples of semigroups which are amalgamation bases in the class of semigroups.