Burch ideals and Burch rings
View/ Open
Issue Date
2020-09-18Author
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
Show full item recordAbstract
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.
Collections
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
Items in KU ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
We want to hear from you! Please share your stories about how Open Access to this item benefits YOU.