Henriques, I.B. orcid.org/0000-0003-3916-7556 and Şega, L.M. (2011) Free resolutions over short Gorenstein local rings. Mathematische Zeitschrift. ISSN 0025-5874
Abstract
Let R be a local ring with maximal ideal m admitting a non-zero element a∈m for which the ideal (0 : a) is isomorphic to R/aR. We study minimal free resolutions of finitely generated R-modules M, with particular attention to the case when m4=0 . Let e denote the minimal number of generators of m . If R is Gorenstein with m4=0 and e ≥ 3, we show that PRM(t) is rational with denominator H R (−t) = 1 − et + et 2 − t 3, for each finitely generated R-module M. In particular, this conclusion applies to generic Gorenstein algebras of socle degree 3.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer-Verlag 2009. The final publication is available at Springer via https://doi.org/10.1007/s00209-009-0639-z |
Keywords: | Primary 13D02; Secondary 13D07 |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Medicine, Dentistry and Health (Sheffield) > School of Health and Related Research (Sheffield) > ScHARR - Sheffield Centre for Health and Related Research |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 30 Aug 2018 11:57 |
Last Modified: | 30 Aug 2018 16:56 |
Published Version: | http://dx.doi.org/10.1112/jlms/jdn027 |
Status: | Published |
Publisher: | Springer |
Refereed: | Yes |
Identification Number: | 10.1112/jlms/jdn027 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:132422 |