✦ LIBER ✦

Borel-fixed ideals and reduction number

✍ Scribed by Lê Tuân Hoa; Ngô Viêt Trung

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 195 KB
Volume: 270
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00367-3

No coin nor oath required. For personal study only.

✦ Synopsis

The aim of this paper is to study the relationship between the reduction number and Borel-fixed ideals in all characteristics. Especially it is shown that r(R/I ) r(R/I lex ), where I lex denotes the unique lex-segment ideal whose Hilbert function is equal to that of I . This solves a recent question by Conca.

📜 SIMILAR VOLUMES

0-Borel Fixed Ideals

✍ Irena Peeva 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 386 KB

an S-regular sequence y , . . . , y . Results of Tate and Gulliksen provide 1 i another important example: the minimal resolution of k over SrQ, for any homogeneous ideal Q in S. In both cases the resolution is a free commu-\* The author is grateful for support by the Alfred P. Sloan Foundation.

Principal Borel ideals and Gotzmann idea

Principal Borel ideals and Gotzmann ideals

✍ V. Bonanzinga 📂 Article 📅 2003 🏛 Springer 🌐 English ⚖ 176 KB

Reduction Numbers of Ideals

✍ Wolmer V. Vasconcelos 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 508 KB

We give general bounds for the reduction numbers of ideals in arbitrary Noetherian rings and multiplicity-dependent bounds for m-primary ideals in a Noetherian local ring (R, m). In the case of polynomial rings over fields the bound is a non-elementary function with four levels of exponentiation; fo

Reduction numbers, Rees algebras and Pfa

Reduction numbers, Rees algebras and Pfaffian ideals

✍ Ian M. Aberbach; Sam Huckaba; Craig Huneke 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 975 KB

A characterization of stable and Borel i

A characterization of stable and Borel ideals

✍ Maria Grazia Marinari; Luciana Ramella 📂 Article 📅 2005 🏛 Springer 🌐 English ⚖ 244 KB

Ideals with bases of unbounded Borel com

Ideals with bases of unbounded Borel complexity

✍ Piotr Borodulin-Nadzieja; Szymon Gła̧b 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 151 KB

We present several naturally defined σ-ideals which have Borel bases but, unlike for the classical examples, these ideals are not of bounded Borel complexity. We investigate set-theoretic properties of such σ-ideals.