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Mosc. Math. J., 2018, Volume 18, Number 2, Pages 205–210 (Mi mmj671)  

A short note on cohomological dimension

Kamal Bahmanpourab, Jafar A'zamia, Ghader Ghasemia

a Faculty of Sciences, Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran
b School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box. 19395-5746, Tehran, Iran

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

Key words and phrases: cohomological dimension, Krull dimension, local cohomology, regular ring, symbolic power.

Full text: http://www.mathjournals.org/.../2018-018-002-002.html
References: PDF file   HTML file

Document Type: Article
MSC: 13D45, 14B15, 13E05
Language: English

Citation: Kamal Bahmanpour, Jafar A'zami, Ghader Ghasemi, “A short note on cohomological dimension”, Mosc. Math. J., 18:2 (2018), 205–210

Citation in format AMSBIB
\Bibitem{BahAzaGha18}
\by Kamal~Bahmanpour, Jafar~A'zami, Ghader~Ghasemi
\paper A short note on cohomological dimension
\jour Mosc. Math.~J.
\yr 2018
\vol 18
\issue 2
\pages 205--210
\mathnet{http://mi.mathnet.ru/mmj671}


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