Some results on self-injective rings and Σ-CS rings

被引：4

作者：

Dinh, HQ ^{[1
]}

Van Huynh, D ^{[1
]}

机构：

[1] Ohio Univ, Dept Math, Athens, OH 45701 USA

来源：

COMMUNICATIONS IN ALGEBRA | 2003年 / 31卷 / 12期

关键词：

CS; (Quasi)-continuous; injective modules; self-injective; Quasi-Frobenius rings;

D O I：

10.1081/AGB-120024867

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A module M is CS if every submodule of M is essential in a direct summand of M. In this note we use the CS condition to provide conditions for semiperfect rings to be self-injective. Further we show that every finitely generated CS right module over a right semi-artinian ring has finite uniform dimension. Using this, we prove that if R is a right semi-artinian ring such that R-R((N)) is CS, then R-R((A)) is also CS for any set A. Moreover, R is then right and left artinian.

引用

页码：6063 / 6077

页数：15

共 28 条

[1]

Anderson F. W., 1992, GRADUATE TEXTS MATH, V13

[2] RINGS IN WHICH EVERY COMPLEMENT RIGHT IDEAL IS A DIRECT SUMMAND [J].