On vanishing of certain Ext modules
Abstract
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 Ext1R(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 m2 kills the 0th local cohomology module Hm0(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.
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