Left Abundant Semigroups

Abstract

The aim of this paper is to study some special lpp-semigroups, namely, the left GC-lpp semigroups. After obtaining some properties and characterizations of such semigroups, we establish some structure theorems of this class of semigroups. In addition, we also consider some special cases. As an application, we describe the structure theorems of IC quasi-adequate semigroups whose idempotent band is a regular band.

Key Words:

• Left abundant semigroups
• Left GC-lpp semigroups
• IC quasi-adequate semigroups
• Regular bands
• Weak semidirect products
• McAister semigroups

AMS Mathematics Subject Classification (2000):

• 20M10

Acknowledgments

The first and the second authors would like to thank Professors J. B. Fountain and M. V. Lawson for mailing them many useful materials concerning the theory of abundant semigroups. The authors also thank the referee for his/her valuable comments and suggestions given to this paper.

This work is supported by the NNSF of China (10071068); the NSF of Yunnan Province (99A0001R); the ECF of Yunnan Province (0011089); the Natural Science Foundation of Jiangxi Province; the Foundation of Education Department of Jiangxi Province; and the Foundation of Jiangxi Normal University and is also partially supported by a UGC(HK) grant (2160187).

Notes

^#Communicated by P. Higgins.