形式三角矩阵环和Morita系统环上的模

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英文题名：Formal Triangular Matrix Rings and Modules over Rings of Morita Contexts 作者：张文汇 论文级别：硕士 学科专业名称：基础数学 学位年度：2003 导师：王利民 学科代码：070101 学位授予单位：西北师范大学 论文提交日期：2003-04-01

摘要

本文从两个不同角度对形式三角矩阵环进行讨论、研究。
     全文分为两章。第一章讨论了形式三角矩阵环的几种环论性质，得到了与PS，CESS，reduced，Baer，Von Neumann正则，强(弱)正则这些环的性质相关的结论。第二章讨论了形式三角矩阵环的扩张——Morita系统环上的模的几种性质。首先构造了Morita系统环上模的子模与商模；其次讨论了这类模的两个基本的子模性质及与此相关的两类模的性质；最后讨论了Morita系统环上模的极大子模和单子模的结构。
In this paper, we discuss the properties of formal triangular matrix rings from two different angles.
    The paper consists of two chapters. In chapter 1, we characterize various ring theoretic properties of formal triangular matrix rings. Some results are obtained on these rings concerning properties such as being respectively PS, CESS, reduced, Baer, von Neumann regular, strong regular or weak regular. In chapter 2, we discuss the properties of modules over rings of Morita contexts that is a extension of formal triangular matrix rings. Firstly, we describe submodules and quotient modules of these modules. Secondly, we discuss two essential properties of submodules of these modules and then use these to characterize two kinds of modules over rings of Morita contexts. Lastly, we think about the construction of maximal(resp. simple) submodules of these modules.

引文

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