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arXiv · 2301.02635

Rings with q-torsionfree canonical modules

Naoki Endo·Laura Ghezzi·Shiro Goto·Jooyoun Hong·Shin-Ichiro Iai·Toshinori Kobayashi·Naoyuki Matsuoka·Ryo Takahashi
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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.

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Naoki Endo, Laura Ghezzi, Shiro Goto, Jooyoun Hong, Shin-Ichiro Iai, Toshinori Kobayashi, Naoyuki Matsuoka, Ryo Takahashi. 2023-01-06. Rings with q-torsionfree canonical modules. https://arxiv.org/abs/2301.02635

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