Some Notes on Abundant Quasi-Ideals of Ample Semigroups

DOI

10.2991/aeece-15.2015.76How to use a DOI?

Keywords

natural partial orders; abundant quasi-ideals; (bi-)order ideals; ample semigroups.

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 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.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Chunhua Li
PY  - 2015/09
DA  - 2015/09
TI  - Some Notes on Abundant Quasi-Ideals of Ample Semigroups
BT  - Proceedings of the International Conference on Advances in Energy, Environment and Chemical Engineering
PB  - Atlantis Press
SP  - 376
EP  - 379
SN  - 2352-5401
UR  - https://doi.org/10.2991/aeece-15.2015.76
DO  - 10.2991/aeece-15.2015.76
ID  - Li2015/09
ER  -