Publications and Research
Document Type
Book Chapter or Section
Publication Date
2025
Abstract
Let A be a Noetherian local ring with canonical module K A . We characterize A when K A 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 K A 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.
Comments
This is the author's preprint of a book chapter originally published in Commutative Algebra: The Mathematical Legacy of Wolmer V. Vasconcelos, edited by Joseph Brennan and Aron Simis, De Gruyter, 2025, pp. 405-426. https://doi.org/10.1515/9783110999365-014
L. Ghezzi was partially supported by the Fellowship Leave from the New York City College of Technology-CUNY (Fall 2022-Spring 2023) and by a grant from the City University of New York PSC-CUNY Research Award Program Cycle 53.