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    Burch ideals and Burch rings

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    Available after: 2026-09-18 (1.348Mb)
    Issue Date
    2020-09-18
    Author
    Dao, Hailong
    Kobayashi, Toshinori
    Takahashi, Ryo
    Publisher
    Mathematical Sciences Publishers (MSP)
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Rights
    © 2020 Mathematical Sciences Publishers
    Metadata
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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.
    URI
    http://hdl.handle.net/1808/33589
    DOI
    https://doi.org/10.2140/ant.2020.14.2121
    Collections
    • Mathematics Scholarly Works [282]
    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

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    KU Libraries
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    785-864-8983

    KU Libraries
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    Lawrence, KS 66045
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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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