Epis and Varieties of Permutative Posemigroups

Abstract

The comprehensive characterization of saturated varieties of semigroups and posemigroups remains an open problem. In this paper, we try to make a significant contribution towards this direction. Firstly, we demonstrate that any finite permutative posemigroup is saturated. Further, our next main result establishes that any regular permutative posemigroup is also saturated. These findings are not only expanding the understanding of saturated posemigroups but also highlights the surjectivity of epis from finite permutative posemigroups and regular permutative posemigroups.