Noether环的一个特征

A Characteristic of Noetherian Rings

主要证明了 :环R为左Noether环当且仅当对任一有限生成左R 模A及任意一集左R 模 {Bi|i∈I} ,有Ext1R(A , i∈IBi)≌ i∈IExt1R(A ,Bi)成立。

In this paper,It is mainly proved that a ring R is left Noetherian if and only if Ext 1 R ( A , i∈I B i )≌ i∈I Ext 1 R ( A , B i ) for every finitely generated left R module A and each family of left R modules{ B i|i∈I }.