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arXiv · 1905.02310

Burch ideals and Burch rings

Hailong Dao·Toshinori Kobayashi·Ryo Takahashi
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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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Hailong Dao, Toshinori Kobayashi, Ryo Takahashi. 2019-05-07. Burch ideals and Burch rings. https://arxiv.org/abs/1905.02310

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