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Rings with q-torsionfree canonical modules
Resource type
Authors/contributors
- Endo, Naoki (Author)
- Ghezzi, Laura (Author)
- Goto, Shiro (Author)
- Hong, Jooyoun (Author)
- Iai, Shin-Ichiro (Author)
- Kobayashi, Toshinori (Author)
- Matsuoka, Naoyuki (Author)
- Takahashi, Ryo (Author)
Title
Rings with q-torsionfree canonical modules
Abstract
Let A be a Noetherian local ring with canonical module KA. We characterize A when KA is a torsionless, reflexive, or q-torsionfree module for an integer q ≥ 3. If A is a Cohen–Macaulay ring, H.-B. Foxby proved in 1974 that the A-module KA 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 quasinormal rings, introduced by W. V. Vasconcelos. We provide several examples as well. ©2025 Walter de Gruyter GmbH,Berlin/Boston.
Book Title
Commutative Algebra
Date
2025
Publisher
Walter de Gruyter GmbH
Pages
405-426
ISBN
978-3-11-100009-1
Citation Key
endoRingsQtorsionfreeCanonical2025
Language
English
Library Catalog
Scopus
Extra
Journal Abbreviation: De Gruyter Proc. Math.
Citation
Endo, N., Ghezzi, L., Goto, S., Hong, J., Iai, S.-I., Kobayashi, T., Matsuoka, N., & Takahashi, R. (2025). Rings with q-torsionfree canonical modules. In Commutative Algebra (pp. 405–426). Walter de Gruyter GmbH. https://doi.org/10.1515/9783110999365-014
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