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Burch ideals and Burch rings
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Description
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.
23 pages, add Example 2.2, Prop 5.5 and Example 5.6
Journal
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- Algebra & Number Theory
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Algebra & Number Theory 14 (8), 2121-2150, 2020-09-18
Mathematical Sciences Publishers
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Keywords
- (weakly) m-full ideal
- Gorenstein ring
- singularity category
- Commutative Algebra (math.AC)
- hypersurface
- singular locus
- Fiber product
- Singularity category
- fiber product
- syzygy
- FOS: Mathematics
- Syzygy
- Representation Theory (math.RT)
- (Weakly) m-full ideal
- Thick subcategory
- 13C13
- Direct summand
- 13H10
- Burch ring
- Singular locus
- Mathematics - Commutative Algebra
- 13C13, 13D09, 13H10
- Burch ideal
- Hypersurface
- direct summand
- thick subcategory
- 13D09
- Mathematics - Representation Theory
Details 詳細情報について
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- CRID
- 1360572092803164928
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- ISSN
- 19447833
- 19370652
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- HANDLE
- 1808/33589
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- Article Type
- journal article
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- Data Source
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- Crossref
- KAKEN
- OpenAIRE