Completely Regular Semigroups And GV-Semigroups

In this thesis, we mainly study H- related congruences on completely regular semigroups and GV- semigroups. It can be divided into three chapters.Chapter 1 is a brief introduction.In Chapter 2 , we study completely regular semigroups . It contains two sections. In Section 1, some basic conceptions and preliminaries about completely regular semigroups are introduced . In Section 2, a concept of H- related congruences on completely regular semigroups is introduced. After that, two equivalent characterizations of H- related congruences are given.Chapter 3 is devoted to the GV- semigroups. It can be divided into 5 sections. In Section 1, we introduce some basic preliminaries about GV- semigroups and some necessary preparations. In Section 2, we give a concept of subdirect product and give a construction theorem of subdirect products for GV- semigroups. In Section 3, we introduce the concepts of pure eventually regular semigroups and pure mappings. We investigate pure covers for GV-semigroups. Section 4 is devoted to the characterizations of some special congruences on GV- semigroups, such as the least group congruence, the idempo-tent separating congruence, the least (left, right) normal band congruence, the least rectangular congruence. In Section 5, we obtain some simple properties on GV- semigroups. The concept of kernel relation K of the congruence lattice is introduced. We show the kernel relation K is a complte ∩- congruence on the congruence lattice. In general, K is not a V- congruence.