2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164385Let R be a Noetherian local ring with the maximal ideal m and dim R=1. In this paper, we shall prove that the module Ext^1_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 0th local cohomology module H_m^0(R). The assertion is no longer true unless v(R) \leq 4. Counterexamples are given. We shall also discuss the relation between our counterexamples and a problem on modules of finite G-dimension.15 pages, minor changes, to appear in Journal of the Mathematical Society of JapanCommutative Algebra13D07 (Primary) 13D05 (Secondary)text