半模Lizuka同余的相关研究

发布时间：2018-04-02 16:05

本文选题：商半模　切入点：Iizuka同余　出处：《江西师范大学》2017年硕士论文

【摘要】：本文主要研究半模Iizuka同余下的一些基本性质与应用,研究了Iizuka同余下商半模的性质和三个基本同构定理;半模Iizuka同余下短伪正合列基本性质及其应用.全文一共分成四个章节:第一章为预备知识,首先介绍了本文一些研究背景与发展形势;然后就是介绍本文中需要用到的相关概念与定理.第二章,在半模上引入Iizuka同余的概念,给出在Iizuka同余下商半模的基本性质,并且根据模范畴的基本同构定理从而研究出Iizuka同余下的商半模的一些性质.第三章,在半模的正合列的基础上,对Iizuka同余下的半模序列进行研拓,引进短伪正合列的概念,并讨论了其相关性质,如:短伪正合列的伪正合性与伪正合列的基本性质.第四章,根据之前所学的半模序列的一些常见定理,如:五引理,三引理,可裂性.用第三章已经证明了的相关性质与定理推导得到短伪正合列一些重要应用.
[Abstract]:In this paper, we study some basic properties and applications of semi-module Iizuka and residue, study the properties and three fundamental isomorphism theorems of Iizuka and residual quotient semimodules, and study the basic properties and applications of semi-module Iizuka and residual short pseudoexact sequence.The whole paper is divided into four chapters: the first chapter is the preparatory knowledge, which firstly introduces the research background and development situation of this paper, and then introduces the relevant concepts and theorems that need to be used in this paper.In chapter 2, we introduce the concept of Iizuka congruence on semimodules, give the basic properties of Iizuka and remainder quotient semimodules, and study some properties of Iizuka and remaining quotient semimodules according to the basic isomorphism theorem of module category.In the third chapter, on the basis of the positive sequence of semi-modules, Iizuka and the remaining semi-module sequences are studied, the concept of short pseudo-positive sequence is introduced, and its related properties are discussed, such as the pseudo-positivity of short pseudo-positive sequence and the basic properties of pseudo-positive sequence.In chapter 4, according to some common theorems of semimodular sequences, such as five lemmas, three lemmas, and cleavage.Some important applications of the short pseudo exact sequence are obtained by using the properties and theorems proved in Chapter 3.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O153.3

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