Rings with q-torsionfree canonical modules
Commutative Algebra
2023-01-12 v2
Abstract
Let A be a Noetherian local ring with canonical module K. We characterize A when K is a torsionless, reflexive, or q-torsionfree module. If A is a Cohen-Macaulay ring, H.-B. Foxby proved in 1974 that the A-module K is q-torsionfree if and only if the ring A is q-Gorenstein. With mild assumptions, we provide a generalization of Foxby's result to arbitrary Noetherian local rings admitting the canonical module. In particular, since the reflexivity of the canonical module is closely related to the ring being Gorenstein in low codimension, we also explore quasi-normal rings, introduced by W. V. Vasconcelos. We provide several examples as well.
Cite
@article{arxiv.2301.02635,
title = {Rings with q-torsionfree canonical modules},
author = {Naoki Endo and Laura Ghezzi and Shiro Goto and Jooyoun Hong and Shin-Ichiro Iai and Toshinori Kobayashi and Naoyuki Matsuoka and Ryo Takahashi},
journal= {arXiv preprint arXiv:2301.02635},
year = {2023}
}
Comments
There is a minor update in Section 6 from the previous version