Reguler and pi-Inverse Monoids under Schützenberger Products

Abstract

In this paper we give a partial answer to the problem which is about the regularity of Schützenberger product in semigroups asked by Gallagher in his thesis [4, Problem 6.1.6]. Furthermore, we determine necessary and sufficient conditions for the new version of the Schützenberger product of monoids which was firstly defined in [1] to be regular and strongly pi-inverse