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Burch ideals and Burch
rings
Hailong Dao, Toshinori Kobayashi and Ryo Takahashi |
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Vol. 14 (2020), No. 8, 2121–2150
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DOI: 10.2140/ant.2020.14.2121
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Abstract |
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We introduce the notion of Burch ideals and Burch rings. They are easy to define, and can be viewed as generalization of many well-known concepts, for example integrally closed ideals of finite colength and Cohen–Macaulay rings of minimal multiplicity. We give several characterizations of these objects. We show that they satisfy many interesting and desirable properties: ideal-theoretic, homological, categorical. We relate them to other classes of ideals and rings in the literature. |
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Dedicated to Lindsay Burch |
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Keywords
Burch ideal, Burch ring, direct summand, fiber product,
Gorenstein ring, hypersurface, singular locus, singularity
category, syzygy, thick subcategory, (weakly) m-full ideal
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Mathematical Subject Classification 2010
Primary: 13C13
Secondary: 13D09, 13H10
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Milestones
Received: 12 June 2019
Revised: 23 November 2019
Accepted: 5 March 2020
Published: 18 September 2020
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Authors |
| Hailong Dao | |
| Department of Mathematics University of Kansas Lawrence, KS United States |
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| Toshinori Kobayashi | |
| Graduate School of Mathematics Nagoya University Nagoya Japan |
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| Ryo Takahashi | |
| Graduate School of Mathematics Nagoya University Nagoya Japan |
Department of Mathematics University of Kansas Lawrence KS United States |
