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.
出处
《内蒙古大学学报(自然科学版)》
CAS
CSCD
北大核心
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)