关于半环正则性的研究

发布时间：2018-01-12 13:32

本文关键词：关于半环正则性的研究　出处：《苏州科技大学》2017年硕士论文　论文类型：学位论文

【摘要】：半环理论是代数学的重要组成部分。在半环理论研究的众多方面中,正则性及其特殊情况的研究是该领域研究的热点之一。半环理论已在形式语言、信息科学及自动机理论等领域得到了较为广泛的应用。本文利用半群的代数理论和方法,研究了半环半直积,圈积的正则性,给出了半环半直积,圈积及其几种特殊情形的正则性的刻画。全文共分为四章。第一章绪论,简要论述国内外有关半环理论发展的概况及与课题相关的研究背景和意义,并介绍本文的主要研究内容和所做的工作。第二章半环的正则性。首先介绍了本文所需的主要概念和结果,然后研究半环的正则性,给出半环为正则半环的等价刻画。第三章半环的半直积。引入半环半直积的概念,研究半环半直积的正则性,给出了半环半直积正则性、逆性和纯整性的特征。得到了若干相关结果。第四章半环半直积的应用。引入半环圈积正则的概念,讨论了几类特殊的正则半环圈积的性质。
[Abstract]:Semiring theory is an important part of algebra. Among the many aspects of semiring theory, regularity and its special situation are one of the hotspots in this field. Semirings theory is already in formal language. Information science and automata theory have been widely used. In this paper, we study the regularity of semidirect product and cycle product by using algebraic theory and method of semigroup, and give semircular semi-direct product. This paper is divided into four chapters. Chapter one is an introduction to the development of semiring theory at home and abroad as well as the research background and significance related to the subject. In chapter 2, the regularity of semirings is introduced. Firstly, the main concepts and results of this paper are introduced, and then the regularity of semirings is studied. This paper gives the equivalent characterization of semirings being regular semirings. In Chapter 3, the semi-direct product of semirings is introduced. The regularity of semi-direct products of semirings is studied, and the regularity of semi-direct products of semirings is given. Some related results are obtained. In Chapter 4th, we introduce the concept of semiring cycle product regularity, and discuss the properties of some special regular semirings product.
【学位授予单位】：苏州科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O153.3

【参考文献】