On Vanishing Of Certain Ext Modules

摘要

Let R be a Noetherian local ring with the maximal ideal m and dim R = 1. In this paper, we shall prove that the module Ext1/R(R/Q, R) does not vanish for every parameter ideal Q in R, if the embedding dimension v(R) of R is at most 4 and the ideal m~2 kills the 0~(th) local cohomology module H_m~O(R). The assertion is no longer true unless v(R) < 4. Counterexamples are given. We shall also discuss the relation between our counterexamples and a problem on modules of finite G-dimension.