Two Classes Of Generalized Regular Semigroups

In this thesis, two classes of generalized regular semigroups are studied. This thesis is divided into two chapters and consists of two integrated papers.In Chapter1, we investigate left GC-lpp semigroups which are common generalizations of left ample semigroups and right inverse semigroups. We prove that the class of left GC-lpp semigroups is a quasi-varity. Further, the structure of free left GC-1pp semigroups is obtained. Also, we investigate the proper cover theorem for left GC-lpp semigroups.In Chapter2, we study a kind of important abundant semigroups, so-called completely T*-simple semigroups. Some characterizations of com-pletely,T*-simple semigroups are obtained, which extend some important results on completely simple semigroups.