Structures Of Two Classes Of Semigroups

In this thesis, we study a class of abundant semigroups whose full sub-semigroups form a chain and a new contruction for inverse semigroups. This thesis is divided into two chapters and consists of two integrated papers.In chapter 1, we study a class of abundant semigroups whose full sub-semigroups form a chain. The aim of this chapter is to investigate abundant â–½fs-semigroups. Some characterizations of such semigroups are obtained. In particular, the structures of completely 0-simple â–½fs-semigroups and primi-tive abundant â–½fs-semigroups satisfying the regularity condition are estab-lished.In chapter 2, The notion of FC-system is introduced. In this chapter, a new construction for inverse semigroups is established in term of Clifford semigroups and fundamental inverse semigroups.