Translator Disclaimer
Spring 2021 On the Hilbert coefficients, depth of associated graded rings and reduction numbers
Amir Mafi, Dler Naderi
J. Commut. Algebra 13(1): 103-115 (Spring 2021). DOI: 10.1216/jca.2021.13.103

Abstract

Let (R,𝔪) be a d-dimensional Cohen–Macaulay local ring, I be an 𝔪-primary ideal of R and let J=(x1,,xd) be a minimal reduction of I. We show that if, for i=0 or 1, Jd1=(x1,,xd1) and n=1λ(In+1Jd1)(JInJd1)=i, then depthG(I)di1. Moreover, we prove that if e2(I)=n=2(n1)λ(InJIn1)2, or if e2(I)=n=2(n1)λ(InJIn1)3 and I is integrally closed, then e1(I)=n=1λ(InJIn1)1, where the integers ei are the Hilbert coefficients of I. In addition, if J is a minimal reduction of I then we prove that the reduction number rJ(I) is independent of J.

Citation

Download Citation

Amir Mafi. Dler Naderi. "On the Hilbert coefficients, depth of associated graded rings and reduction numbers." J. Commut. Algebra 13 (1) 103 - 115, Spring 2021. https://doi.org/10.1216/jca.2021.13.103

Information

Received: 1 November 2017; Revised: 17 September 2019; Accepted: 16 September 2019; Published: Spring 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.1216/jca.2021.13.103

Subjects:
Primary: 13A30, 13D40, 13H10

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
13 PAGES

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

SHARE
Vol.13 • No. 1 • Spring 2021
Back to Top