Abstract
Let (R,m) be a commutative Noetherian regular local ring of dimension d and I be a proper ideal of R such that mAssR(R/I) = AsshR(I). It is shown that the R- module Hht(I)I (R) is I-cofinite if and only if cd(I,R) = ht(I). Also we present a sufficient condition under which this condition the R-module HiI (R) is finitely generated if and only if it vanishes.
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