Some Studies On Semilattice Decompositions Of Semigroups

This thesis is divided into three chapters.In Chapter 1,we introduce some definitions and lemmas,fix some notation which is used in the remaining part.In Chapter 2,we discuss semilattices of monoids and prove that a semigroup is a semilattice of monoids if and only if it is a quasi-strong semilattice of these monoids.We also discuss some basic properties of S-indecomposable semigroups and their applications,and give an equivalent description of left groups.Fundamental semilattices of a kind of Rees matrix semigroups are investigated at the end of this chapter.In Chapter 3,we give the definition of good homomorphisms between any two semigroups which have regular semilattice decompositions and characterize such homomorphisms.