Free summands of syzygies of modules over local rings
type: Item
instance of: scholarly article
title: Free summands of syzygies of modules over local rings
zbMATH Open document ID: 1184.13041
author: Bart Snapp
published in: Journal of Pure and Applied Algebra
publication date: 2010-04-22T00:00:00Z
review text: The author gives the following criterion for a commutative, noetherian, local ring to be Cohen-Macaulay: Theorem 2.4. A local ring \((A, \mathfrak m, k)\) is Cohen--Macaulay if and only if for some \(i > 0\), \(\mathrm{Syz}_i (A/x)\) has a free summand for some system of parameters \(x\) that form part of a minimal set of generators for \(\mathfrak m\).
reviewed by: Olaf Teschke
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13D22
zbMATH DE Number: 5697062
MaRDI profile type: Publication
full work available at URL: j.jpaa.2009.12.023
OpenAlex ID: W2107611608
cites work: On the Canonical Element Conjecture
cites work: Q3360288
cites work: Some restrictions on the maps in minimal resolutions
cites work: A remarkable property of the (co) syzygy modules of the residue field of a nonregular local ring
cites work: Q4488212
cites work: Syzygy modules with semidualizing or G-projective summands
DOI: 10.1016/J.JPAA.2009.12.023
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description: scientific article; zbMATH DE number 5697062