Let [Formula: see text] be a commutative Noetherian ring, [Formula: see text] an ideal of [Formula: see text] and [Formula: see text] a finitely generated R-module with dimR(M) = d. Denote by depth[Formula: see text] the depth of [Formula: see text] in [Formula: see text]. In [C. Huneke and V. Trivedi, The height of ideals and regular sequences, Manuscr. Math. 93 (1997) 137–142], Huneke and Trivedi proved that if [Formula: see text] is a quotient of a regular ring then there exists a finite subset [Formula: see text] of [Formula: see text] such that [Formula: see text] Denote by [Formula: see text] the [Formula: see text]th pseudo support of [Formula: see text] defined by Brodmann and Sharp [On the dimension and multiplicity of local cohomology modules, Nagoya Math. J. 167 (2002) 217–233]. In this paper, we prove that if [Formula: see text] is closed for all [Formula: see text] then the above formula of [Formula: see text] holds true, where [Formula: see text]. In particular, if [Formula: see text] is a quotient of a Cohen–Macaulay local ring then [Formula: see text]. We also give some examples to clarify the results.
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