On Transversals Of Quasi-adequate #-abundant Semigroups

In this thesis, we mainly study quasi-ideal adequate transversals and multiplicative adequate transversals of quasi-adequate #-abundant semigroups.It can be divided into three chapters.Chapter 1 ,we study quasi-adequate #-abundant semigroups. Section 1 is a brief introduction.In Section 2, some basic conceptions and preliminaries about quasi-adequate #-abundant semigroups are introduced .In Section 3,we obtain some properties of quasi-adequate #-abundant semigroups, and confirm the existence of the minimum adequate good congruence .In Chapter 2 , we study quasi-ideal adequate transversals . It contains six sections. In Section 1,some background about transversals are introduced . In Section 2, some basic conceptions and preliminaries about quasi-adequate are introduced . In Section 3,some properties of I and A are character-ized.In Section 4,we proved that any two quasi-ideal adequate transversals of quasi-adequate #-abundant semigroups are isomorphic.In Section 5,we proved that the product of any two quasi-ideal adequate transversals is also a quasi-ideal adequate transversal.In Section 6,some properties of a quasi-adequate #-abundant semigroup with a quasi-ideal adequate transversal are characterized.Chapter 3 is devoted to multiplicative adequate transversals of a quasi-adequate #-abundant semigroup.It can be divided into 3 sections. In Section 1, we introduce some basic preliminaries about multiplicative adequate transver- sals and some necessary preparations. In Section 2, some properties of I and A are characterized. In Section 3, an embedding theorem is given.