Modules of \(G\)-dimension zero over local rings of depth two
Let \(R\) be a commutative Noetherian local ring. The concept of Gorenstein dimension of a module was introduced by Auslander and its finiteness characterizes the Gorenstein property of the ring. The main result of the paper under review proves that if \(R\) is a henselian non-Gorenstein local ring of depth two with a non-free \(R\)-module of \(G\)-dimension zero, then the category of modules of \(G\)-dimension zero, \({\mathcal G}(R)\), is not contravariantly finite in mod-\(R\), i.e. not every \(M\in \text{mod-}R\) has an \({\mathcal G}(R)\)-precover.
scientific article; zbMATH DE number 2140258