Abstract

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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.