SOME NEW CHARACTERIZATIONS OF QUASI-FROBENIUS RINGS BY USING PURE-INJECTIVITY

被引：1
|
作者：
Moradzadeh-Dehkordi, Ali [1 ,2 ]
机构：
[1] Univ Shahreza, Fac Basic Sci, POB 86149-56841, Shahreza, Iran
[2] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran
来源：
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2020年 / 57卷 / 02期
关键词：
Right pure-injective ring; right Artinian ring; quasi-Frobenius ring; MODULES;
D O I：
10.4134/BKMS.b190247
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A ring R is called right pure-injective if it is injective with respect to pure exact sequences. According to a well known result of L. Melkersson, every commutative Artinian ring is pure-injective, but the converse is not true, even if R is a commutative Noetherian local ring. In this paper, a series of conditions under which right pure-injective rings are either right Artinian rings or quasi-Frobenius rings are given. Also, some of our results extend previously known results for quasi-Frobenius rings.
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页码：371 / 381
页数：11
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