次内射模的特征

journal6 ›› 2003, Vol. 24 ›› Issue (2): 77-78.

次内射模的特征

（湖北民族学院数学系，湖北恩施 445000）

出版日期:2003-06-15 发布日期:2012-11-07
作者简介:詹建明(1972-)，男，湖北黄冈人，硕士，湖北民族学院数学系讲师，主要从事同调代数研究.
基金资助:
湖北省教育厅重点科研基金资助项目(2002X10)

Characterizations of Subinjective Modules

(Dept.of Math,Hubei Institute for Nationalities Enshi,Hubei 445000)

Online:2003-06-15 Published:2012-11-07

摘要/Abstract

摘要：引进次内射维数的概念，给出次内射模的一些性质，并用次内射模及维数刻划了次半单环、Noether环及遗传环的性质.主要结论为：(ⅰ)左R-模M是次内射模SIdRM=0.(ⅱ)环R为次半单环SID(R)=0.(ⅲ)环R为Noether环每个次内射模是内射模.

关键词： 次内射模, 次内射维数, 次半单环, Noether环, 遗传环

Abstract: This paper introduces the concept of subinjective dimension and obtains the nature of subinjective modules.Moreover subsemisimple ring,noether ring and hereditary ring are characteristiced.The main results are:(ⅰ)Any left R-module M is subinjective module if and only if SIdRM=0.(ⅱ)A ring R is subsemisimple ring if and only if SID(R)=0.(ⅲ)A ring R is Noether if and only if every subinjective module is injective.

Key words: subinjective modules, subinjective dimension；subsemisimple rings, noether rings, hereditary rings

詹建明. 次内射模的特征[J]. journal6, 2003, 24(2): 77-78.

ZHAN Jian-Ming. Characterizations of Subinjective Modules[J]. journal6, 2003, 24(2): 77-78.