Some Notes on Abundant Quasi-Ideals of Ample Semigroups
Chunhua Li · 2015
The aim of this paper is to study ample semigroups by using natural partial orders on abundant semigroups.After giving some properties and characterizations of abundant quasi-ideals on ample semigroups, we prove that there exists an idempotent-separating good congruence on an abundant quasi-ideal M of an arbitrary ample semigroup S, which can be extended to an idempotent-separating good congruence on S. In this paper, we develop an approach to the structure of ample semigroups inspired by the semigroup algebra theory of Mario petrich for inverse semigroups.