On weak-injective modules over integral domains

被引：8

作者：

Fuchs, Laszlo ^{[2
]}

Lee, Sang Bum ^{[1
]}

机构：

[1] Sangmyung Univ, Dept Math, Seoul 110743, South Korea

[2] Tulane Univ, Dept Math, New Orleans, LA 70118 USA

来源：

JOURNAL OF ALGEBRA | 2010年 / 323卷 / 07期

关键词：

Torsion-free; Flat; Pure-injective and weak-injective modules; Enochs-cotorsion modules; Flat cover; Weak-injective envelope; Almost perfect domain; Weak dimension;

D O I：

10.1016/j.jalgebra.2010.02.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that a weak-injective module over an integral domain need not be pure-injective (Theorem 2.3). Equivalently, a torsion-free Enochs-cotorsion module over an integral domain is not necessarily pure-injective (Corollary 2.4). This solves a well-known open problem in the negative. In addition, we establish a close relation between flat covers and weak-injective envelopes of a module (Theorem 3.1). This yields a method of constructing weak-injective envelopes from flat covers (and vice versa). Similar relation exists between the Enochs-cotorsion envelopes and the weak dimension <= 1 covers of modules (Theorem 3.2). (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：1872 / 1878

页数：7

共 12 条

[1]

Bazzoni S., 2003, Colloq. Math, V95, P285, DOI [10.4064/cm95-2-11, DOI 10.4064/CM95-2-11]

[2] Cotorsion pairs generated by modules of bounded projective dimension [J].