Cohen-Macaulay dimension of modules over Noetherian rings
type: Item
instance of: scholarly article
title: Cohen-Macaulay dimension of modules over Noetherian rings
zbMATH Open document ID: 1098.13013
published in: Rocky Mountain Journal of Mathematics
publication date: 2006-01-24T00:00:00Z
review text: The paper gives a criterion for an arbitrary Noetherian ring to be Cohen-Macualay. The authors prove that a Noetherian ring \(R\) is Cohen-Macaulay if and only if, for all finitely generated \(R\)-modules \(M\), the Cohen-Macaulay dimension is finite. This extends a similar criterion known for local rings.
reviewed by: Goutam Mukherjee
Mathematics Subject Classification ID: 13D05
Mathematics Subject Classification ID: 13C15
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13D22
zbMATH DE Number: 5000995
author: Javad Asadollahi
author: Shokrollah Salarian
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069674
OpenAlex ID: W1993942178
cites work: Stable module theory
cites work: Homological Dimension in Noetherian Rings.
cites work: Support varieties and cohomology over complete intersections
cites work: Complete intersection dimension
cites work: Q4274969
cites work: Restricted homological dimensions and Cohen-Macaulayness
cites work: On homological dimensions
cites work: Vanishing of \(Ext^ i_ R(M,R)\)
cites work: Construction of modules with finite homological dimensions
DOI: 10.1216/RMJM/1181069674
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description: scientific article; zbMATH DE number 5000995