Moscow Mathematical Journal

Volume 18, Issue 2, April–June 2018 pp. 205–210.

A Short Note on Cohomological Dimension

Authors: Kamal Bahmanpour (1), Jafar A'zami (2), and Ghader Ghasemi (3)
Author institution:(1) Faculty of Sciences, Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran; and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box. 19395-5746, Tehran, Iran
(2) Faculty of Sciences, Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran
(3) Faculty of Sciences, Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran

Summary:

Let (R, m) be a Noehterian regular local ring and p be a prime ideal of R. In this paper it is shown that if the set S := {n ∈ ℕ: R/p⁽ⁿ⁾ is Cohen–Macaulay} is infinite, then cd(p, R) = height(p).

2010 Math. Subj. Class. 13D45, 14B15, 13E05.

Keywords: Cohomological dimension, Krull dimension, local cohomology, regular ring, symbolic power.

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