About Two Classes of Right Abundant Semigroups

In this thesis, we have studied two classes of right abundant semigroups. This thesis is divided into two chapters and each chapter is an integrated paper.In Chapter 1, we introduce the concept of FR-systems and then establish the structure of the general F-rpp semigroups by using FR-systems. As an application, we obtained the characterizations of F-abundant semigroups. In addition, an example is provided to iIiustrate that strongly F-rpp semigroups form a proper subclass of F-rpp semigroups. This gives a negative answer of an open problem on F-rpp semigroups.Chapter 2 is devoted to IC quasi-adequate semigroups. We prove that each IC quasi-adequate semigroup with left regular band of idempotents has a proper cover. In particular, the structure of proper covers of IC quasi-adequate semigroups with left regular band of idempotents are established. As an application, we obtain some characterizations of proper IC quasi-adequate semigroups with left regular band of idempotents.