Studies On Abundant Semigroups

In this thesis, some special subclasses of abundant semigroups are studied. The thesis is divided into three chapters.In Chapter 1, we investigate the cancellative monoids. We establish the structure of a class of cancellative monoids, so-called normal cancellative monoids. Furthermore, we introduce the concept of viscous extension of cancellative monoids, and point out. that any normal cancellative monoid can be constructed by the outer automorphism group of a group. Lastly, the semidirect product characterization of normal cancellative monoids is investigated. As its application, we characterize a special case of cancellative monoids, named uniform cancellative monoids.Chapter 2 is dedicated to the study of quasi-adequate semigroups whose band of idempotents is the direct product of a rectangular band and aω-chain, called quasi-adequate semigroups of type E-chain. We establish the structure of idempotent connected D*-simple quasi-adequate semigroups of type RBI and in which contains precisely one regular D-class by developing Bruck-Reilly extensions.The aim of Chapter 3 is to study idempotent-connected quasi-adequate semigroups whose band of idempotents is a left regular band. We establish the structure of this kind of semigroups. In addition, we also describe the structure of good congruences on an idempotent-connected quasi-adequate semigroup whose band of idempotents is a left regular band.