Translator Disclaimer
2020 Burch ideals and Burch rings
Hailong Dao, Toshinori Kobayashi, Ryo Takahashi
Algebra Number Theory 14(8): 2121-2150 (2020). DOI: 10.2140/ant.2020.14.2121

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.

Citation

Download Citation

Hailong Dao. Toshinori Kobayashi. Ryo Takahashi. "Burch ideals and Burch rings." Algebra Number Theory 14 (8) 2121 - 2150, 2020. https://doi.org/10.2140/ant.2020.14.2121

Information

Received: 12 June 2019; Revised: 23 November 2019; Accepted: 5 March 2020; Published: 2020
First available in Project Euclid: 12 November 2020

MathSciNet: MR4172703
Digital Object Identifier: 10.2140/ant.2020.14.2121

Subjects:
Primary: 13C13
Secondary: 13D09 , 13H10

Keywords: (weakly) m-full ideal , Burch ideal , Burch ring , direct summand , fiber product , Gorenstein ring , Hypersurface , singular locus , singularity category , syzygy , thick subcategory

Rights: Copyright © 2020 Mathematical Sciences Publishers

JOURNAL ARTICLE
30 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.14 • No. 8 • 2020
MSP
Back to Top