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Burch ideals and Burch rings

Dao, Hailong
; 
Kobayashi, Toshinori
; 
Takahashi, Ryo
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Abstract
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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Date
2020-09-18
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Publisher
Mathematical Sciences Publishers (MSP)
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Mathematics Scholarly Works
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Available after: 2026-09-18
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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
Citation
Dao, H., Kobayashi, T., Takahashi, R. (2020). Burch ideals and Burch rings. Algebra & Number Theory, Vol. 14 (2020), No. 8, 2121–2150. DOI: 10.2140/ant.2020.14.2121
URI
https://hdl.handle.net/1808/33589
DOI
10.2140/ant.2020.14.2121
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