# 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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