Doherty, B, Faber, E orcid.org/0000-0003-2541-8916 and Ingalls, C (2016) Computing global dimension of endomorphism rings via ladders. Journal of Algebra, 458. pp. 307-350. ISSN 0021-8693
Abstract
This paper deals with computing the global dimension of endomorphism rings of maximal Cohen–Macaulay (=MCM) modules over commutative rings. Several examples are computed. In particular, we determine the global spectra, that is, the sets of all possible finite global dimensions of endomorphism rings of MCM-modules, of the curve singularities of type for all n, for and and compute the global dimensions of Leuschke's normalization chains for all ADE curves, as announced in [12]. Moreover, we determine the centre of an endomorphism ring of a MCM-module over any curve singularity of finite MCM-type.
In general, we describe a method for the computation of the global dimension of an endomorphism ring , where R is a Henselian local ring, using -approximations. When is a MCM-module over R and R is Henselian local of Krull dimension ≤2 with a canonical module and of finite MCM-type, we use Auslander–Reiten theory and Iyama's ladder method to explicitly construct these approximations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Elsevier Inc. This is an author produced version of a paper published in Journal of Algebra. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Endomorphism rings of finite global dimension, Maximal Cohen–Macaulay modules, Auslander–Reiten theory, Ladder, Noncommutative resolution |
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) |
Depositing User: | Symplectic Publications |
Date Deposited: | 27 Jun 2018 14:20 |
Last Modified: | 29 Jun 2018 18:13 |
Published Version: | https://doi.org/10.1016/j.jalgebra.2016.03.020 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jalgebra.2016.03.020 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:132503 |