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
CAMILLO, VP
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1977, 69 (02) : 337 - 338
[2] A NOTE ON PERFECT SELF-INJECTIVE RINGS
CLARK, J
VANHUYNH, D
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 1994, 45 (177) : 13 - 17
[3] FAITH C, 1976, ALGEBRA, V2
[4] ON DUAL RINGS AND THEIR MODULES
HAJARNAVIS, CR
NORTON, NC
[J]. JOURNAL OF ALGEBRA, 1985, 93 (02) : 253 - 266
[5] KATO T, 1985, TOHKU MATH J, V93, P253
[6] A GENERALIZATION OF QUASI-FROBENIUS RINGS
OSOFSKY, BL
[J]. JOURNAL OF ALGEBRA, 1966, 4 (03) : 373 - &
[7] Tachikawa, 1956, MATH Z, V65, P414, DOI [10.1007/BF01473890, DOI 10.1007/BF01473890]
[8] SELF-INJECTIVE RINGS
UTUMI, Y
[J]. JOURNAL OF ALGEBRA, 1967, 6 (01) : 56 - &

← 1 →