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Regular F-Abundant Semigroups
Authors:Xiaojiang Guo  K P Shum  Liang Zhang
Institution:1. Department of Mathematics , Jiangxi Normal University , Nanchang, Jiangxi, China xjguo@jxnu.edu.cn;3. Faculty of Sciences , The Chinese University of Hong Kong, Shatin, N. T , Hong Kong, China;4. Department of Applied-Mathematics , Tongji University , Shanghai, China
Abstract: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
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