Coherent rings and absolutely pure precovers

被引：14

作者：

Dai, Guocheng ^{[1
]}

Ding, Nanqing ^{[2
]}

机构：

[1] Sichuan Normal Univ, Coll Math & Software Sci, Chengdu, Sichuan, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2019年 / 47卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Absolutely pure module; coherent ring; direct limit; precovering class; ENVELOPES;

D O I：

10.1080/00927872.2019.1595637

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we prove that a precovering class is closed under direct limits provided that is closed under direct products and pure submodules. As a corollary, we get that a ring R is left coherent if and only if the class of absolutely pure left R-modules is a precovering class.

引用

页码：4743 / 4748

页数：6

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