Faber, E orcid.org/0000-0003-2541-8916 (2020) Trace Ideals, Normalization Chains, and Endomorphism Rings. Pure and Applied Mathematics Quarterly, 16 (4). pp. 1001-1025. ISSN 1558-8599
Abstract
In this paper we consider reduced (non-normal) commutative noetherian rings R.With the help of conductor ideals and trace ideals of certain R-modules we deduce a criterion for a reflexive R-module to be closed under multiplication with scalars in an integral extension of R. Using results of Greuel and Knörrer this yields a characterization of plane curves of finite Cohen–Macaulay type in terms of trace ideals.
Further, we study one-dimensional local rings (R,m) such that that their normalization is isomorphic to the endomorphism ring EndR(m): we give a criterion for this property in terms of the conductor ideal, and show that these rings are nearly Gorenstein. Moreover, using Grauert–Remmert normalization chains, we show the existence of noncommutative resolutions of singularities of low global dimensions for curve singularities.
Metadata
Item Type: | Article |
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Authors/Creators: | |
Copyright, Publisher and Additional Information: | © by International Press of Boston, Inc. All rights reserved. This is an author produced version of an article published in Pure and Applied Mathematics Quarterly. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Funding Information: | Funder Grant number EU - European Union 789580 |
Depositing User: | Symplectic Publications |
Date Deposited: | 04 Feb 2020 16:54 |
Last Modified: | 30 Nov 2020 14:01 |
Status: | Published |
Publisher: | International Press |
Identification Number: | 10.4310/PAMQ.2020.v16.n4.a4 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:154104 |