Regular F-Abundant Semigroups

ABSTRACT

The investigation of regular F-abundant semigroups is initiated. In fact, F-abundant semigroups are generalizations of regular cryptogroups in the class of abundant semigroups. After obtaining some properties of such semigroups, the construction theorem of the class of regular F-abundant semigroups is obtained. In addition, we also prove that a regular F-abundant semigroup is embeddable into a semidirect product of a regular band by a cancellative monoid. Our result is an analogue of that of Gomes and Gould on weakly ample semigroups, and also extends an earlier result of O'Carroll on F-inverse semigroups.

Keywords:

• IC-semigroup
• Regular band
• Regular F-abundant semigroup
• Quasi-adequate semigroup
• Weakly ample semigroup

Mathematics Subject Classification (2000):

• 20M10

ACKNOWLEDGMENTS

The authors would like to thank the referee for giving them valuable advice toward this paper.

This author Xiaojiang Guo is supported by the NNSF of China (10071068), the NSF of Jiangxi Province, the SF of Education Department of Jiangxi Province, the Foundation of Jiangxi Normal University

The research of the second author is partially supported by RGC (CUHK) grant #2160210(02/04).

communicated by P. Higgins.