广义局部上同调模的消去性

On Vanishing of Generalized Local Cohomology Modules

在交换Noether环R中引进一种新的模类——广义k-上合冲模类.证明当i充分大后,相对于R的一个理想α的广义局部上同调模Hiα(M,N)等于零,其中M是具有有限投射维数的有限生成模,N是一个广义k-上合冲模.作为应用,给出Gorenstein环的一种新刻画.

In this paper,we introduce the new class of generalized k-cosyzygy modules over a commutative Noether ring R. It is shown that the generalized local cohomology module Hiα（ M,N） with respect to an ideal α of R vanishes for i sufficiently large,where M is a finitely generated R-module with finite projective dimension and N is a generalized k-cosyzygy module. As an application,we give a criteria for Gorenstein rings.