CN-环  

CN-rings

作　　者：熊丽丽[1] 李男杰[1] 魏俊潮[1] 

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2011年第2期7-9,共3页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10771182);江苏省普通高校研究生科研创新项目(CX09B-309Z)

摘　　要：研究CN-环的一些性质,主要证明了如下结果:①设R为CN-环和左SF-环,则R为强正则环;②R为约化环当且仅当R是左NPP环和CN-环;③CN-环的次直积也是CN-环;④设R为CN-环,则R为弱reversible环,反之未必;⑤设R为CN-环,每个单奇异左R-模Wnil-内射,则R为约化环;⑥设R为CN-环,每个单奇异左R-模YJ-内射,则R为约化的弱正则环.This paper shows the following results： ① If R is a CN-ring and left SF-ring,then R is a strongly regular ring;② R is a reduced ring if and only if R is a CN-ring and left NPP ring;③ The subdirect product of CN-rings is also a CN-ring;④ If R is a CN-ring,then R is a weakly reversible ring,but the converse is not true;⑤ If R is a CN-ring whose simple singular left modules are Wnil-injective,then R is a reduced ring;⑥ If R is a CN-ring whose simple singular left modules are YJ-injective,then R is a reduced weakly regular ring.

关 键 词：CN-环 幂零元 中心元 约化环 Wnil-内射模 

分 类 号：O153.3[理学—数学] O154[理学—基础数学]