Envelopes and covers by modules of finite FP-injective and flat dimensions

被引：50

作者：

Mao, Lixin

Ding, Nanqing

机构：

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

[2] Nanjing Univ, Dept Basic Courses, Nanjing Inst Technol, Nanjing 210093, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2007年 / 35卷 / 03期

基金：

中国博士后科学基金; 中国国家自然科学基金; 高等学校博士学科点专项科研基金;

关键词：

cotorsion theory; n-cotorsion module; (Pre)Cover; ( Pre) Envelope;

D O I：

10.1080/00927870601115757

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a ring, n a fixed non-negative integer and FIn (F-n) the class of all right (left) R-modules of FP-injective (flat) dimension at most n. We prove that (FIn, FIn perpendicular to) is a perfect cotorsion theory if R is a right coherent ring with FP-id (R-R) <= n. This result was proven by Aldrich, Enochs, Jenda, and Oyonarte in Noetherian case. The modules in F-n(perpendicular to) are also studied. Some applications are given.

引用

页码：833 / 849

页数：17

共 31 条

[1] Covers and envelopes in Grothendieck categories: Flat covers of complexes with applications [J].