Regular and π-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 deter-mine 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 -inverse.