On self-injective perfect rings

被引：6

作者：

Herbera, D

Shamsuddin, A

机构：

[1] AMER UNIV BEIRUT,DEPT MATH,BEIRUT,LEBANON

[2] UNIV AUTONOMA BARCELONA,DEPT MATEMAT,E-08193 BARCELONA,SPAIN

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 1996年 / 39卷 / 01期

关键词：

perfect rings; self-injective rings; quasi-Frobenius rings; injective envelope; semi-local rings;

D O I：

10.4153/CMB-1996-007-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a left and right perfect right self-injective ring. It is shown that if the radical of R is countably generated as a left ideal then R is quasi-Frobenius. It is also shown that the same conclusion can be drawn if r(A boolean AND B) = r(A) + r(B) for all left ideals A and B of R.

引用

页码：55 / 58

页数：4

共 8 条

[1] MODULES WHOSE QUOTIENTS HAVE FINITE GOLDIE DIMENSION [J].