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A NOTE ON COHOMOLOGICAL DIMENSION OVER COHEN-MACAULAY RINGS

  • Bagheriyeh, Iraj (Department of Mathematics Faculty of Sciences University of Mohaghegh Ardabili) ;
  • Bahmanpour, Kamal (Department of Mathematics Faculty of Sciences University of Mohaghegh Ardabili) ;
  • Ghasemi, Ghader (Department of Mathematics Faculty of Sciences University of Mohaghegh Ardabili)
  • Received : 2019.02.10
  • Accepted : 2019.07.26
  • Published : 2020.03.31

Abstract

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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