On simple singular GP-injective modules

被引：42

作者：

Kim, NK ^{[1
]}

Nam, SB

Kim, JY

机构：

[1] Kyung Hee Univ, Dept Math, Suwon 449701, South Korea

[2] Kyung Hee Univ, Inst Nat Sci, Suwon 449701, South Korea

来源：

COMMUNICATIONS IN ALGEBRA | 1999年 / 27卷 / 05期

关键词：

D O I：

10.1080/00927879908826551

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate von Neumann regularity of rings whose simple singular right R-modules are GP-injective. It is proved that a ring R is strongly regular iff R is a weakly right duo ring whose simple singular right R-modules are GP-injective. And it is also shown that R is either a strongly right bounded ring or a zero insertive ring in which every simple singular right R-module is GP-injective are reduced weakly regular rings. Several known results are unified and extended.

引用

页码：2087 / 2096

页数：10

共 26 条

[1] A CLASS OF RINGS HAVING ALL SINGULAR SIMPLE MODULES INJECTIVE
ALIN, JS
ARMENDAR.EP
[J]. MATHEMATICA SCANDINAVICA, 1968, 23 (02) : 233 - &
[2] BACCELLA G, 1984, REND SEMIN MAT U PAD, V72, P117
[3] Birkenmeier G. F., 1993, P BIENN OH STAT DEN, P102
[4] Regularity conditions and the simplicity of prime factor rings
Birkenmeier, GF
Kim, JY
Park, JK
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 1997, 115 (03) : 213 - 230
[5] A CONNECTION BETWEEN WEAK REGULARITY AND THE SIMPLICITY OF PRIME FACTOR RINGS
BIRKENMEIER, GF
KIM, JY
PARK, JK
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 122 (01) : 53 - 58
[6] RINGS OVER WHICH EVERY SIMPLE MODULE IS RATIONALLY COMPLETE
BROWN, SH
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1973, 25 (04): : 693 - 701
[7] WEAKLY REGULAR-RINGS
CAMILLO, V
XIAO, YF
[J]. COMMUNICATIONS IN ALGEBRA, 1994, 22 (10) : 4095 - 4112
[8] DING NQ, 1994, MATH JPN, V40, P191
[9] FAITH C, 1984, LONDON MATH SOC LECT, V88
[10] Gupta V., 1977, MATH J OKAYAMA U, V19, P123

← 1 2 3 →