Burch ideals and Burch rings
Burch ideals and Burch rings
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DOI：
10.2140/ant.2020.14.2121
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发表时间：
2019-05
影响因子：
1.3
通讯作者：
Hailong Dao;Toshinori Kobayashi;Ryo Takahashi
中科院分区：
文献类型：
--
作者：
Hailong Dao;Toshinori Kobayashi;Ryo Takahashi
我们引入了Burch理想和Burch环的概念。它们很容易定义，并且可以被看作是许多著名概念的推广，例如有限长度的整闭理想和最小重数的科恩-麦考利环。我们给这些对象的几个特征。我们表明，他们满足许多有趣的和可取的性质：理想理论，同调，分类。我们将它们与其他类的理想和环的文献。
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.