(n,d)平坦左R-模的几个性质

Several Properties of(n,d)Flat Left R-Module

设R是任意带单位元的结合环,一个左R-模K被称为是左(n,d)平坦的。如果对任意的n表现的右R-模M,均有Tord+1(M,K)=0。给出了(n,d)平坦左R-模的几个性质,用(n,d)平坦左R-模对右(n,0)环和右n-凝聚环作了一些刻画。证明了:环R是右(n,0)环,当且仅当任何以(n,0)平坦左R-模为中间项的左R-模短正合列是n纯。环R是右n-凝聚环,当且仅当任何左R-模短正合列0→A→B→C→0,如果B C是(n,d)平坦的,则A也是(n,d)平坦的。

Let R be any associative ring with identity. A left R-module K is called left （n ,d） flat, if Tord ＋ 1 （ M, K ） = 0 for every n-presented right R-module M. Some properties of （ n, d ）flat left R-module are given, and use them to characterize right n-coherent rings and right （n ,0） rings. R is right （n ,0）ring if and only if every short exact sequence with （n, d ）flat pure. Ring R is right n-coherent if and only if A is（ n ,d）flat with respect to exact sequence 0→A→B→C→0 with B and C （n ,d）flat.