Modules that detect finite homological dimensions

Abstract

We study homological properties of test modules that are, in principle, modules that detect finite homological dimensions. The main outcome of our results is a generalization of a classical theorem of Auslander and Bridger: we prove that, if a commutative Noetherian complete local ring R admits a test module of finite Gorenstein dimension, then R is Gorenstein.

to appear in Kyoto Journal of Mathematics

References in corpus (1)

• Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension

Cited by in corpus (4)

• Homological dimensions of rigid modules
• Vanishing of (co)homology over deformations of Cohen-Macaulay local rings of minimal multiplicity
• Integrally closed $\mathfrak{m}$-primary ideals have extremal resolutions
• On the vanishing of (co)homology for modules admitting certain filtrations