Certain Types Of Semigroup Congruence

In this paper,we describe congruences on V-regular semigroups and V-orthodox semigroups by kernel normal systems approach and kernel-trace ap-proach, and study eventually regular congruences on E-inversive semigroups by kernel normal systems approach.It is composed of four chapters.Chapter 1 is introduction.In chapter 2,we describe congruences on V-regular semigroups.The relative basic concepts and necessary preliminaries are given,some properties of congruences are studied,the concepts of the kernel normal systems and the congruences paris of V-regular semigroups are introduced,and congruences on V-regular semigroups are described by the kernel normal systems approach and the kernel-trace approach,respectively.In chapter 3,we introduce a special class of V-regular semigroups,namely V-orthodox semigroups,and explore their properties.We also introduce the concepts of the kernel normal systems and the congruences paris on V-orthodox semigroups,and describe congruences on V-orthodox semigroups by the kernel normal systems approach and the kernel-trace approach.In chapter 4,we generalize the concept of regular congruences on E-inversive semigroups,and introduce the concept of eventually regular congruences on E-inversive semigroups.We study eventually regular congruences on E-inversive semigroups by the kernel normal systems approach.We introduce a special class of E-inversive semigroups,namely E-inversive weakly E-semigroups.As a collary,eventually regular congruences on E-inversive weakly E-semigroups can also be obtained similarly.