Regular F-Abundant Semigroups |
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Authors: | Xiaojiang Guo K P Shum Liang Zhang |
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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 |
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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. |
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Keywords: | IC-semigroup Regular band Regular F-abundant semigroup Quasi-adequate semigroup Weakly ample semigroup |
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