Some Applications Of Refined Semilattices Of Semigroups

The main topic is some applications of refined semilattices of semigroups in the study of properties and structures of semigroups.We mainly determine the constructions of good homomorphisms between any two regular orthocryptou semigroups and refined semilattice structures of locally orthodox regular cryptogroups. The whole paper consists of three chapters.We present the basic definitions and properties of semigroups in Chapter 1.Especially, some relative contents about completely regular semigroups and semilattice of semigroups are introduced.And then,we give some notations and terminology which are used in what follows.In Chapter 2,we first show that the refined semilattice decomposition of any regular orthocryptou semigroup into rectangular u-semigroups is unique.Then using such a structure description,we investigate good homomorphisms between any two regular orthocryptou semigroups.Chapter 3 is devoted to show that a semigroup is a locally orthodox regular cryptogroup if and only if it can be uniquely expressed as a refined semilattices of completely simple semigroups.Such structure description can be specialized to left (respectively,right) quasinormal cryptogroups.The strong semilattice construction of normal cryptogroups is thus a special case.