Left SF-rings and regular rings

被引：18

作者：

Zhou, Haiyan ^{[1
]}

机构：

[1] Nanjing Normal Univ, Dept Math, Nanjing 210097, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2007年 / 35卷 / 12期

基金：

中国国家自然科学基金; 高等学校博士学科点专项科研基金;

关键词：

GW-ideals; left SF-rings; strongly regular rings; von Neumann regular rings; W-ideals;

D O I：

10.1080/00927870701511632

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A ring R is called a left (right) SF-ring if all simple left (right) R-modules are flat. It is known that von Neumann regular rings are left and right SF-rings. lit this article, we study the regularity of left SF-rings and we prove the following. 1) if R is a left SF-ring whose all complement left (right) ideals are W-ideals, then R is strongly regular; 2) if R is a left SF-ring whose all maximal essential right ideals are GW-ideals, then R is regular.

引用

页码：3842 / 3850

页数：9

共 14 条

[1]

Faith C., 1981, ALGEBRA 1 RINGS MODU

[2]

Goodearl KR, 1974, RING THEORY NONSINGU

[3]

Hirano Y., 1979, HIROSHIMA MATH J, V9, P137

[4] INJECTIVITY AND FLATNESS OF CERTAIN CYCLIC MODULES [J].

RAMAMURTHI, VS .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 48 (01) :21-25

[5]

Rege M. B., 1986, Math. Japonica, V31, P927

[6]

YUE CMR, 1980, MATH J OKAYAMA U, V22, P151

[7]

YUE CMR, 1982, COMMENT MATH U CAROL, V23, P427

[8]

YUE CMR, 1988, ACTA MATH VIETNAMICA, V23, P71

[9]

Zhang J., 1992, ACTA MATH VIETNAMICA, V17, P157

[10]

Zhang J., 1998, SE ASIAN B MATH, V22, P231

← 1 2 →