Gorenstein homological dimension and Ext-depth of modules
type: Item
instance of: scholarly article
title: Gorenstein homological dimension and Ext-depth of modules
zbMATH Open document ID: 1174.13015
author: Amir Mafi
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2009-10-09T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1251832379
review text: Let \((R,\mathfrak m, k)\) be a commutative noetherian local ring. It is well-known that, \(R\) is regular if and only if the flat dimension of \(k\) is finite. In this paper, the author shows that \(R\) is Gorenstein if and only if the Gorenstein flat dimension of \(k\) is finite. Also he shows that if \(R\) is a Cohen-Macaulay ring and \(M\) is a Tor-finite \(R\)-module [see \textit{T. Sharif} and \textit{S. Yassemi}, Commun. Algebra 30, No. 2, 869--875 (2002; Zbl 1097.13510)] of finite Gorenstein flat dimension, then the depth of the ring is equal to the sum of the Gorenstein flat dimension and Ext-depth of \(M\).
Mathematics Subject Classification ID: 13C11
Mathematics Subject Classification ID: 13C13
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 5612298
zbMATH Keywords: Gorenstein flat dimension
zbMATH Keywords: Cohen-Macaulay ring
zbMATH Keywords: depth
reviewed by: Siamak Yassemi
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5612298