期刊论文

Mininjective Modules,Minflat Modules and Some Rings

中文

内蒙古大学学报（自然科学版）

Acta Scientiarum Naturalium Universitatis Neimongol

1000-1638

2004

35

4

367-371

10.3969/j.issn.1000-1638.2004.04.003

湖北省教育厅重点科研项目(2003X024)；

本校为其他机构

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***模和极小平坦模的一些刻划,并用极小***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 r...