Rings with the dual of the isomorphism theorem

被引：136
|
作者：
Nicholson, WK [1 ]
Campos, ES
机构：
[1] Univ Calgary, Dept Math, Calgary, AB T2N 1N4, Canada
[2] Univ Malaga, Dept Algebra, Malaga 29080, Spain
来源：
JOURNAL OF ALGEBRA | 2004年 / 271卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
D O I：
10.1016/j.jalgebra.2002.10.001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A ring R satisfies the dual of the isomorphism theorem if R/Ra congruent to 1(a) for all elements a of R, where l(a) denotes the left annihilator. We call these rings left morphic. Examples include all unit regular rings and certain left uniserial local rings. We show that every left morphic ring is right principally injective, and use this to characterize the left perfect, right and left morphic rings. (C) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码：391 / 406
页数：16
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