STRONGLY GORENSTEIN FLAT MODULES

被引：130

作者：

Ding, Nanqing ^{[1
]}

Li, Yuanlin ^{[2
]}

Mao, Lixin ^{[3
]}

机构：

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

[2] Brock Univ, Dept Math, St Catharines, ON L2S 3A1, Canada

[3] Nanjing Inst Technol, Inst Math, Nanjing 211167, Peoples R China

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2009年 / 86卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

strongly Gorenstein flat module; Gorenstein flat module; precover; pre-envelope; cotorsion theory; INJECTIVE MODULES; COHERENT RINGS; COVERS; DIMENSIONS; ENVELOPES;

D O I：

10.1017/S1446788708000761

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, strongly Gorenstein flat modules are introduced and investigated. An R-module M is called strongly Gorenstein flat if there is an exact sequence ... -> P-1 -> P-0 -> P-0 -> P-1 -> ... of projective R-modules with M = ker(P-0 -> P-1) such that Hom(-, F) leaves the sequence exact whenever F is a flat R-module. Several well-known classes of rings are characterized in terms of strongly Gorenstein flat modules. Some examples are given to show that strongly Gorenstein flat modules over coherent rings lie strictly between projective modules and Gorenstein flat modules. The strongly Gorenstein flat dimension and the existence of strongly Gorenstein flat precovers and pre-envelopes are also studied.

引用

页码：323 / 338

页数：16

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