Naturally Ordered Abundant Semigroups in Which Each Idempotent Has a Greatest Inverse

Abstract

The aim of this article is to study naturally ordered abundant semigroups in which every idempotent has a greatest inverse. After obtaining some characterizations, their structure is established.

Keywords:

• Abundant semigroup
• Greatest inverse
• Naturally ordered semigroup

Mathematics Subject Classification (2000):

• 20M10
• 06F05

ACKNOWLEDGMENT

The authors would like to thank Professor D. Easdown for revising their English and making a number of editorial improvements to the article.

The work of the first author is jointly supported by the Natural Science Foundation of Jiangxi Province, the Science Foundation of the Education Department of Jiangxi Province and the Foundation of Jiangxi Normal University, China.

The work of the second author is supported by the Natural Science Foundation of China and the Natural Science Foundation of Guangdong Province, China.

Notes

Communicated by D. Easdown.