On weak-injective modules over integral domains

JOURNAL OF ALGEBRA

卷:323

Article

Fuchs, Laszlo²  Lee, Sang Bum¹ 

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

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

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;   

DOI  :  10.1016/j.jalgebra.2010.02.005

来源: Elsevier

【 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.

【 授权许可】

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