Burch ideals and Burch rings

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.

arXiv comment23 pages, add Example 2.2, Prop 5.5 and Example 5.6

References in corpus (2)

• Free resolutions over short Gorenstein local rings
• Local rings with quasi-decomposable maximal ideal

Cited by in corpus (1)

• On a class of Burch ideals and a conjecture of Huneke and Wiegand