A new example of strongly $pi$ inverse monoids

Abstract

In [1], Ate¸s defined the semidirect product version of the Schützenberger product for any two monoids, and examined its regularity. Since this is a new product and there are so many algebraic properties that need to be checked for it, in this paper we determine necessary and sufficient conditions for this new version to be strongly $pi$-inverse, and then give some results.