极小内射模、极小平坦模与某些环  

Mininjective Modules,Minflat Modules and Some Rings

作　　者：朱占敏[1] 

机构地区：[1]湖北民族学院数学系,湖北恩施445000

出　　处：《内蒙古大学学报（自然科学版）》2004年第4期367-371,共5页Journal of Inner Mongolia University：Natural Science Edition

基　　金：湖北省教育厅重点科研项目(2003X024)

摘　　要：称一个右R-模M是极小平坦的,如果对任一极小左理想I,自然同态M RI→M RR是单的.环R称为左极小遗传的,如果R的每个极小左理想都是投射的.环R称为左极小正则的,如果R的每个极小左理想都是RR的直和项.环R称为左极小凝聚的,如果R的每个极小左理想是有限表现的.给出了极小内射模和极小平坦模的一些刻划,并用极小内射模和极小平坦模刻划了极小遗传环、极小正则环和极小凝聚环.Let R be a ring.A right R-module M is said to be minflat if for every minimal left ideal I the canonical homomorpism M_RI→M_RR is monic.R is called left minhereditary,if every minimal left ideal of R is projective.R is called left minregular,if every minimal left ideal of R is a direct summand.R is called mincoherent,if every minimal left ideal of R is finitely presented.Some characterizations of mininjective modules and minflat modules are given respectively.Minhereditary rings are characterized by mininjective modules,and minregular rings,and mincoherent rings are characterized by mininjective modules and minflat modules.

关 键 词：极小内射模 极小平坦模 极小遗传环 极小正则环 极小凝聚环 

分 类 号：O153.3[理学—数学]