Test modules, weakly regular homomorphisms and complete intersection dimension
Abstract
We prove that if a local ring admits a (pd-)test module of finite complete intersection dimension, then it is a complete intersection ring. This answers, positively, a question proposed by Celikbas, Dao and Takahashi. To this aim, we first investigate another question raised by Celikbas and Sather- Wagstaff concerning ascent properties of (pd-)test complexes under weakly regular homomorphisms.
Cite
@article{arxiv.1911.11290,
title = {Test modules, weakly regular homomorphisms and complete intersection dimension},
author = {Ehsan Tavanfar},
journal= {arXiv preprint arXiv:1911.11290},
year = {2022}
}
Comments
To appear in the Journal of Commutative Algebra. The section about alternative proofs was removed from the submitted version to the journal. For references to the results appearing in the journal version, please follow the journal format (the journal version will be uploaded in the journal's website before assignment of a DOI). Some minor typos corrected with respect to the previous version