[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b190165

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)

Publication Information

Bulletin of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 275-280 More about this Journal

Abstract

Let (R, m) be a Noetherian local Cohen-Macaulay ring and I be a proper ideal of R. Assume that β_R(I, R) denotes the constant value of depth_R(R/Iⁿ) for n ≫ 0. In this paper we introduce the new notion γ_R(I, R) and then we prove the following inequalities: β_R(I, R) ≤ γ_R(I, R) ≤ dim R - cd(I, R) ≤ dim R/I. Also, some applications of these inequalities will be included.

Keywords

Canonical module; Cohen-Macaulay ring; cohomological dimension; local cohomology; Noetherian ring;

Citations & Related Records

Times Cited By KSCI : 4 (Citation Analysis)

Reference
Cited By KSCI

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