Structures Of Some Semigroups

In this dissertation, we study the structures of some semigroups. The main idea is to describe the sructures of some special completely regular semigroups by subdirect product and spined product, to describe the structures of generialized regular semigroups by generialized Green relations and in terms of the structures of the set of some idempotents in generialized regular semigroups.Regular semigroups, particularly completely regular semigroups are a class of very important semigroups. In this paper,the structures of some orthodox completely regular semigroups will be described and then will be generialized to some generialized regular semigroups accordingly. There are two chapters.In the first chapter, we deal with LR—quasinormal semigroups and LR—quasinormal — Ehresmann semigroups. We introduce the concept of LR—quasinormal semigroups, i.e.. the completely regular semigroups with the set of idempotents being LR—quasinormal bands, obtaining some structure theorems of such semigroups. Related results obtained by M.K.Sen, Shamik Ghosh and Sumana Pal on LR—C semigroups are generialized. Then we intrduce the concept of LR—quasinormal—Ehresmann semigroups, which can be viewed as the generalization of LR—quasinormal semigroups in the range of W—liberal semigroups.In the second chapter, we discuss the structures of LR—seminormal — Ehresmann semigroups and LR—seminormal semigroups . Firstly , we give the definition of LR-seininormal—Ehresmann semigroups, i.e., the orthodox U—liberal semigroups with the set of projections being LR—seminormal bands, obtaining the semi-spined product structures and the A— product structures of such semigroups.Secondly, we define LR—seminormal semigroups, i.e., the completely regular semigroups with the set of idempotents being LR -seminormal bands, obtaining some structure theorems. Virtually LR-seminormal-Ehresmann semigroups can be viewed as the generialization of LR—seminormal semi-groups in the range of U—liberal semigroups.