A NOTE ON COHOMOLOGICAL DIMENSION OVER COHEN-MACAULAY RINGS

Let (R, m) be a Noetherian local Cohen-Macaulay ring and I be a proper ideal of R. Assume that βR(I, R) denotes the constant value of depthR(R/In) for n ≫ 0. In this paper we introduce the new notion γR(I, R) and then we prove the following inequalities: βR(I, R) ≤ γR(I, R) ≤ dim R - cd(I, R) ≤ dim...

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Published in:Taehan Suhakhoe hoebo 2020, Vol.57 (2), p.275-280
Main Authors: Bagheriyeh, Iraj, Bahmanpour, Kamal, Ghasemi, Ghader
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Bahmanpour, Kamal
Ghasemi, Ghader
description Let (R, m) be a Noetherian local Cohen-Macaulay ring and I be a proper ideal of R. Assume that βR(I, R) denotes the constant value of depthR(R/In) for n ≫ 0. In this paper we introduce the new notion γR(I, R) and then we prove the following inequalities: βR(I, R) ≤ γR(I, R) ≤ dim R - cd(I, R) ≤ dim R/I. Also, some applications of these inequalities will be included.
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title A NOTE ON COHOMOLOGICAL DIMENSION OVER COHEN-MACAULAY RINGS
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