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arXiv · 1207.5869

Modules that detect finite homological dimensions

Olgur Celikbas·Hailong Dao·Ryo Takahashi
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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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Olgur Celikbas, Hailong Dao, Ryo Takahashi. 2012-07-25. Modules that detect finite homological dimensions. https://doi.org/10.1215/21562261-2642404

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