余撓模與n-余撓模.pdf

1、西北師范大學(xué)碩士學(xué)位論文余撓模與n-余撓模姓名：任偉申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：劉仲奎2009-05AbstractThere are two sections in this paper.In section 1, it is firstly proved that when R is an IF ring, M is a co-torsion module if and only if it can be decomp

2、osed into a direct sum ofan injective module and a reduced cotorsion module. Moreover, such de-composition is unique up to isomorphism. Following that, we discuss somerelations between cotorsion envelopes and injective e

3、nvelopes of modules,define the concept of minimal cotorsion envelopes and prove that cotor-sion envelopes and minimal cotorsion envelopes of modules are equivalentprovided that any factor modules of flat modules are flat

4、. Finally, somecharacterizations of von Neumann regular ring and perfect ring are givenin view of covers and envelopes of modules.In section 2, we discuss some properties of n-cotorsion modules, describen-flat covers ( n