(n, d)-Injective covers, n-coherent rings, and (n, d)-rings

被引：6
|
作者：
Li, Weiqing [1 ]
Ouyang, Baiyu [1 ]
机构：
[1] Hunan Normal Univ, Coll Math & Comp Sci, Key Lab High Performance Comp & Stochast Informat, Minist Educ China, Changsha 410081, Hunan, Peoples R China
来源：
CZECHOSLOVAK MATHEMATICAL JOURNAL | 2014年 / 64卷 / 02期
关键词：
cover; envelope; n-coherent ring; (n; d)-injective; d)-ring; MODULES;
D O I：
10.1007/s10587-014-0101-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is known that a ring R is left Noetherian if and only if every left R-module has an injective (pre)cover. We show that (1) if R is a right n-coherent ring, then every right R-module has an (n, d)-injective (pre)cover; (2) if R is a ring such that every (n, 0)-injective right R-module is n-pure extending, and if every right R-module has an (n, 0)-injective cover, then R is right n-coherent. As applications of these results, we give some characterizations of (n, d)-rings, von Neumann regular rings and semisimple rings.
引用
收藏
页码：289 / 304
页数：16
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