![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
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.
Mathematics Subject Classification (2000):
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.