Regular F-Abundant Semigroups.

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. [ABSTRACT FROM AUTHOR]