Depth of associated graded rings via Hilbert coefficients of ideals

2003/04/08 by Alberto Corso, Corso, Alberto, Claudia Polini +3
Mathematics · #13A30 #13B21 #13D40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13A30 #msc:13B21 #msc:13D40

paper · pdf · doi:10.48550/arxiv.math/0304111

17 pages. J. Pure and Applied Algebra, to appear

arxiv created 2003/04/08 · openalex publication_date 2003/04/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a local Cohen-Macaulay ring (R, \mathfrak m), we study the interplay between the integral closedness -- or even the normality -- of an \mathfrak m-primary R-ideal I and conditions on the Hilbert coefficients of I. We relate these properties to the depth of the associated graded ring of I.

Related

• Hilbert Coefficients and Depth of the Associated Graded Ring of an Ideal
• On the Hilbert coefficients, depth of associated graded rings and\n reduction numbers
• The depth of the associated graded ring of ideals with any reduction number
• On the first generalized Hilbert coefficient and depth of associated graded rings
• Integrally closed ideals of reduction number three