Gorenstein homological dimension and Ext-depth of modules
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 \(M\).
scientific article; zbMATH DE number 5612298