Notes on cotorsion modules

被引：34

作者：

Mao, LX ^{[1
]}

Ding, NQ

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

[2] Nanjing Inst Technol, Dept Basic Course, Nanjing, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2005年 / 33卷 / 01期

基金：

高等学校博士学科点专项科研基金; 中国国家自然科学基金;

关键词：

cotorsion module; cotorsion envelope; flat cover; perfect ring; von Neumann regular ring;

D O I：

10.1081/AGB-200041029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a ring. A right R-module C is called cotorsion if Ext(R)(1)(F, C) = 0 for any flat right R-module F. In this paper, we first give some results on cotorsion envelopes that are analogous to those on injective envelopes. Then we characterize those rings R for which every cotorsion right R-module is A-injective, where A is a nonemptry collection of right ideals of R. Finally, some new characterizations of right perfect rings and von Neumann regular rings are given.

引用

页码：349 / 360

页数：12

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