Some criteria for the Cohen-Macaulay property and local cohomology
type: Item
instance of: scholarly article
title: Some criteria for the Cohen-Macaulay property and local cohomology
zbMATH Open document ID: 1183.13025
author: Amir Mafi
publication date: 2009-11-11T00:00:00Z
review text: Let \(R\) be a commutative noetherian ring and \(A\) be a proper ideal of \(R\). The author obtains a characterization of Cohen-Macaulay rings using relative homological algebra. It is shown that \(R\) is Cohen-Macaulay if and only if for any module \(M\), height of \(P\) is less or equal to the Gorenstein flat dimension of \(M\) for all prime idea \(P\) with the 0-th Bass number of \(M\) in \(P\), \(\mu_0(P,M)\), not zero. Moreover, if \((R,{\mathcal M})\) is a complete local ring, the filter depth of \(M\) in \(A\), i.e. the length of a maximal filter regular sequence of \(M\) in \(A\), is greater of equal to \(d\), the depth of \(D(H_{\mathcal M}^i(M))\geq i-1\) for all \(2\leq i<d\) and \(H_{\mathcal M}^i(M)\not=0\), then \(D(H_{\mathcal M}^d(M))\) is a Cohen-Macaulay \(R\)-module of dimension \(d\).
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13C11
zbMATH DE Number: 5629547
zbMATH Keywords: Cohen Macaulay rings
zbMATH Keywords: Gorenstein flat modules
zbMATH Keywords: local cohomology modules
zbMATH Keywords: filter regular sequences
reviewed by: Blas Torrecillas
describes a project that uses: Macaulay2
MaRDI profile type: Publication
full work available at URL: s10114-009-7418-y
OpenAlex ID: W2396158370
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DOI: 10.1007/S10114-009-7418-Y
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5629547