| 毕竟正则半群及其子半群系统的若干研究 |
| Alternative Title | Some studies on eventually regular semigroups with a system of subsemigroups
|
| 王宇 |
| Thesis Advisor | 罗彦锋
|
| 2010-05-30
|
| Degree Grantor | 兰州大学
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| Place of Conferral | 兰州
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| Degree Name | 博士
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| Keyword | 毕竟正则半群
完全毕竟正则半群
理想
幂等元
半格分解
完全毕竟正则子半群格
全子半群格
|
| Abstract | 本文主要研究毕竟正则半群与它的子半群系统之间的各种关系, 得到了一系列有意义的最新结果.
全文共分为五章:
第一章为引言部分. 介绍了半群及其子半群系统的研究背景、
研究内容和目前的研究进展, 并且系统地介绍本文
在这一领域的具体结果.
第二章介绍半群及其子半群系统领域的一些基本概念、术语和记号,
并且给出格理论中的相关概念和结论. 最后, 给出
本文需要经常用到的基本理论.
第三章研究一类特殊类型的毕竟正则半群-----完全毕竟正则半群及其完全毕竟正则子半群格之间的相互联系.
着重讨论, 完全毕竟正则子半群格满足不同格类型时,
完全毕竟正则半群的结构. 本章分别刻画, 完全毕竟正则子半群格是分配格、
下半分配格、0-下半分配格、0-模格和链的完全毕竟正则半群的结构.
第四章探讨毕竟正则半群与它的全子半群格之间的关系. 分别给出,
毕竟正则半群满足全子半群格是
0-下半分配格、分配格和链的充分必要条件, 并且具体刻画了
两类特殊的毕竟正则半群类, 即强毕竟逆半群和纯正完全毕竟
正则半群在它们的全子半群格是
0-下半分配格、分配格和链时的结构.
第五章讨论毕竟正则半群与它的一些特殊子半群(子集) 之间的相互关系.
主要研究两者在性质上的相互作用. 本章考虑的特殊子半群(子集)
的类型有: 毕竟正则半群的幂等元集,
毕竟正则半群的各种理想和毕竟正则半群中由幂等元集所生成的子半群.
另外, 还研究了毕竟正则半群上的半格分解,
给出了左群的诣零扩张的半格的最新结果. |
| Other Abstract | This doctoral thesis is mainly devoted to do some
researches on eventually regular semigroups with a system of their
subsemigroups. Some meaningful results are obtained.The thesis
consists of five chapters.Chapter 1 provides a
brief introduction. The background and development of the theory
concerning semigroups with their subsemigroup systems are
comprehensively presented. Moreover, the main results of the thesis
are systematically introduced .In Chapter 2, we introduce some fundamental definitions, notations
and terminologies that will be used in the sequel. In addition,
several necessary preliminary materials on the lattice theory are
covered as well.
Chapter 3 is devoted to study the
relationships between epigroups and their subepigroup lattices. The
main aim of the chapter is to describe the structure of epigroups
for which the subepigroup lattices satisfy some lattice-theoretic
conditions. Among various of lattice-theoretic conditions, we
investigate distributive lattice, meet semidistributive lattice,
0-semidistributive lattice, 0-modular lattice and chain,
respectively.In Chapter 4, we explore the connections
between eventually regular semigroups and their full subsemigroup lattices. The sufficient and necessary conditions for eventually
regular semigroups whose full subsemigroup lattices are
0-semidistributive lattices, distributive lattices and chains,
respectively, are presented. Moreover, the particularly transparent
structural descriptions are given in the case of strongly eventually
inverse semigroups and of orthoepigroups.
The aim of Chapter 5 is to discuss various inter-relationships
between eventually regular semigroups and their particular
subsemigroups (subsets). We mainly study the mutual reactions
between the properties owned by eventually regular semigroups and
those owned by their particular subsemigroups (subsets), including
the set of idempotents, ideals and subsemigroups generated by the
set of idempotents. Furthermore, semilattice decompositions of
semigroups are considered and some new results on characterizations
of semilattices of nil-extensions of left groups are given. |
| URL | 查看原文
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| Language | 中文
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| Document Type | 学位论文
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| Identifier | https://ir.lzu.edu.cn/handle/262010/225614
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| Collection | 数学与统计学院
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Recommended Citation
GB/T 7714 |
王宇. 毕竟正则半群及其子半群系统的若干研究[D]. 兰州. 兰州大学,2010.
|
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