Ikeda-Nakayama rings

被引:33
作者
Camillo, V [1 ]
Nicholson, WK
Yousif, MF
机构
[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA
[2] Univ Calgary, Dept Math, Calgary, AB T2N 1N4, Canada
[3] Ohio State Univ, Dept Math, Lima, OH 45804 USA
基金
加拿大自然科学与工程研究理事会;
关键词
D O I
10.1006/jabr.1999.8217
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A ring R is called a right Ikeda-Nakayama ring (right IN-ring) if the left annihilator of the intersection of any two right ideals is the sum of the two left annihilators. In this paper we show that if R is a right IN-ring and A and B are right ideals of R that are complements of each other, there exists an idempotent e in R such that A = eR and B = (1 - e)R. As a consequence we show that R is right selfinjective if and only if M-2(R) is a right IN-ring. It is also shown that R is a dual ring if and only if R is a left and right IN-ring and the dual of every simple right R-module is simple. Finally, we prove that R is quasi-Frobenius if and only if R is a left perfect, left and right IN-ring, extending work on both selfinjective rings and dual rings. Several examples are provided to show that our results are non-trivial extensions of the known results on the subject. (C) 2000 Academic Press.
引用
收藏
页码:1001 / 1010
页数:10
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