【作者】 张爱平；

【导师】 张玉芬；

【作者基本信息】 山东师范大学 ， 基础数学， 2005， 硕士

【摘要】 本论文主要研究某些半群的结构,其主要思想是利用次直积和织积来刻画某些特殊的完全正则半群的结构,利用广义格林关系和根据广义正则半群的幂等元的集合的某个子集的结构来研究广义正则半群的结构。 正则半群特别是完全正则半群是一种极其重要的半群,本文将研究某些纯整的完全正则半群的结构,并将其推广到相应的广义正则半群上。全文共分两章。 第一章,主要对LR-拟正规半群及LR-拟正规-Ehresmann半群的结构进行了描述。介绍了LR-拟正规半群的概念,即幂等元的集合为LR-拟正规带的完全正则半群,得到了一些这种半群的结构定理,推广了M.K.Sen,Shamik Ghosh和Sumana Pal关于LR-C半群的结果。然后又介绍了LR-拟正规-Ehresmann半群的概念,它是LR-拟正规半群在u-丰富半群范围内的推广。 第二章,主要刻画了LR-半正规-Ehresmann半群及LR-半正规半群的结构。首先给出了LR-半正规-Ehresmann半群的定义,即投射集U,(U(?)E(S))为LR-半正规带的纯整u-丰富半群,描述了这种半群的半织积结构和Δ-积结构。然后定义了LR-半正规半群,即幂等元的集合为LR-半正规带的完全正则半群,得到相应的结构定理。其中LR-半正规-Ehresmann半群可被看作为LR-半正规半群在u-丰富半群范围内的推广。更多还原

【Abstract】 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.更多还原