【作者】 徐晓利；

【导师】 王芳贵；

【作者基本信息】 四川师范大学 ， 基础数学， 2010， 硕士

【摘要】 本文主要利用相对w-包络和w-模理论的方法研究任意的R-模,得到了一些较w-模更为一般的性质和结果.论文分为两章.在第一章中,我们首先引入了相对w-子模和相对w-包络的概念.并对其性质做了深入的研究,给出了相对w-子模成为准素子模的充要条件是(A:M)w≠R或者对于任意的J∈GV(R).有J (?)(A：M).通过局部化的方法我们得到：有限型模可以表示为它的某个有限生成子模的相对w-包络,并且有极大相对w-子模.接着证明了本章的主要定理——有限型模成为w-Xoether模当且仅当它有相对w-子模的升链条件.第二章的内容主要是围绕w-多余子模展开的.首先我们证得：单模与GV-挠模是GV-不可约模：w-Artin模的每个相对w-子模都包含一个GV-不可约子模.且w-Artin模关于极大w-理想的局部化恰好为Artin模.进而分别讨论了模的w-多余子模和w-Jacobson根.并给出了相应的例子.最后我们证得：对于满足条件每一个非平凡的相对w-子模包含在一个极大相对w-子模中的模.其w-多余子模与w-Jacobson根的子模是一一对应的.更多还原

【Abstract】 In this paper, the methods of w-envelopes and w-module theory are employed to investigate an arbitrary R-module.We obtain some more general properties and results than w-module.This thesis is divided into two chapters.In Chapter 1.we firstly introduce two notions:relative w-submodule and relative w-envelope. and discuss some properties of them. Then we get that sufficient and necessary conditions for a primary submodule to be a relative w-submodule is (A:M)w,≠R or for an arbitrary GV-ideal.J∈(A:M).By the way of localization we obtain that any finite type module can be expressed as the relative w-envelope of one of its finite submodules and always has maximal relative w-submodule.At last,the main theorem of this chapter is shown that a finite type module is a w-Noether module if and only if it has the ascending chain condition on relative w-submodule.In Chapter 2.we do our work around w-superfluous submodules.We prove that simple module and GV-torsion module are GV-irreducible modules,each real relative w-submodule of w-Artin module includes a GV-irreducible submodule, and its localization about w-ideal is Artin-module. Moreover,we discussed w-superfluous submodules and w-Jacobson radicals separately. At the same time corresponding examples are also given.Finally, it is found that for the module satisfying the condition that each real relative w-submodule contained in a maximal relative w-submodule.there is a one to one correspondence between w-superfluous submodules and the submodules of w-Jacobson radical.更多还原