Modules that detect finite homological dimensions
classification
🧮 math.AC
math.RT
keywords
finitehomologicalmodulesdetectdimensionsgorensteintestadmits
read the original 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.
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