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Structure theory of generalized regular semigroups.

机译：广义正则半群的结构理论。

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摘要

In this thesis, we study the structure theory of generalized regular semigroups, including quasiregular semigroups, abundant semigroups and rpp semigroups.; The first part of the thesis is divided into two chapters. In Chapter 1, we obtain a structure theorem for left Clifford semigroups by using left quasi-direct product of left regular bands and Clifford semigroups. The concept of left quasi-direct product developed in this chapter is a new technique in studying structure theory of semigroups. In Chapter 2, we provide a method of construction for generalized orthogroups and as a consequence, the structure theorem of Petrich for orthogroups follows as an immediate corollary of our theorem on generalized orthogroups.; The second part of the thesis is composed of Chapters 3 to 6. The main purpose of these chapters is to study abundant semigroups. In Chapter 3, we show that an L* -inverse semigroup can be described as a left cohort product of a type A semigroup Gamma and a left regular band B with respect to a left cohort mapping. This result generalizes the structure theorem of Yamada for left inverse semigroups. In Chapter 4, we establish the structure theorem for quasi*-inverse semigroups by using the sandwich cohort product of semigroups. In particular, we prove that a semigroup is a quasi*-inverse semigroup if and only if it is a spined product of an L* -inverse semigroup and an R* -inverse semigroup. In Chapter 5 we show that a superabundant semigroup can be represented by a semilattice of normalized Rees matrix semigroups over some cancellative monoids. This last result extends the well known result of Petrich on completely regular semigroups.; In the third part of the thesis, we concentrate on the structure of rpp semigroups. In Chapter 7, a structure theorem for right C-rpp semigroups is given. We show in Chapter 8 that a semigroup S is an rpp semigroup with left central idempotents if and only if S is a strong semilattice of left cancellative right stripes.
机译：本文研究了广义正则半群的结构理论，包括准正则半群，丰富半群和rpp半群。论文的第一部分分为两章。在第一章中，我们通过使用左正则带和Clifford半群的左拟直接积，获得了左Clifford半群的结构定理。本章提出的左准直接乘积的概念是研究半群结构理论的一种新技术。在第二章中，我们为广义正交群提供了一种构造方法，因此，佩特里奇对正交群的结构定理是我们对广义正交群定理的直接推论。本文的第二部分由第三章至第六章组成。这些章节的主要目的是研究丰富的半群。在第3章中，我们显示L *逆半群可以描述为相对于左群映射的A型半群Gamma和左规则带B的左群乘积。该结果推广了Yamada关于左逆半群的结构定理。在第四章中，我们利用半群的三明治队列产品建立了拟*逆半群的结构定理。特别地，当且仅当半群是L *逆半群和R *逆半群的自旋乘积时，我们证明半群是准*逆半群。在第5章中，我们显示了一个超丰裕的半群可以由一些可取消半体上的归一化Rees矩阵半群的半格表示。最后的结果扩展了Petrich在完全规则的半群上的众所周知的结果。在论文的第三部分，我们集中在rpp半群的结构上。在第七章中，给出了正确的C-rpp半群的结构定理。我们在第8章中证明，当且仅当S是左可消除右条纹的强半格时，半群S是具有左中心等幂的rpp半群。

著录项

  • 作者

    Ren, Xueming.;

  • 作者单位

    The Chinese University of Hong Kong (People's Republic of China).;

  • 授予单位 The Chinese University of Hong Kong (People's Republic of China).;
  • 学科 Mathematics.
  • 学位 Ph.D.
  • 年度 2002
  • 页码 133 p.
  • 总页数 133
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数学;
  • 关键词

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