Ratliff-Rush filtration, regularity and depth of higher associated graded modules. II.

DOI10.1016/j.jpaa.2016.07.008zbMath1349.13010arXiv0808.3258OpenAlexW2046587957MaRDI QIDQ338229

Tony Joseph Puthenpurakal

Publication date: 4 November 2016

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.3258

zbMATH Keywords

local cohomologyHilbert coefficientsgeneralized Cohen-Macaulay moduleRatliff-Rush filtrationRees-algebraStückrad-Vogel invariantsuperficial sequence

Mathematics Subject Classification ID

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Local cohomology and commutative rings (13D45) Homological functors on modules of commutative rings (Tor, Ext, etc.) (13D07) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items (9)

Bounds for the reduction number of primary ideal in dimension three ⋮ Ratliff-Rush filtration, Hilbert coefficients and reduction number of integrally closed ideals ⋮ The strong Rees property of powers of the maximal ideal and Takahashi-Dao's question ⋮ Bockstein cohomology of associated graded rings ⋮ Results on the Hilbert coefficients and reduction numbers ⋮ Bounds for Hilbert coefficients ⋮ On asymptotic depth of integral closure filtration and an application ⋮ Cohen-Macaulay local rings with \(e_2 = e_1 - e + 1\) ⋮ On coefficient ideals

Cites Work

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• Ratliff-Rush filtration, regularity and depth of higher associated graded modules. I
• Hilbert functions of filtered modules
• Hilbert functions and symbolic powers
• Cohen-Macaulay local rings of dimension two and an extended version of a conjecture of J. Sally
• Hilbert coefficients of Hilbert filtrations
• Hilbert coefficients of a Cohen-Macaulay module.
• Hilbert coefficients of integrally closed ideals
• The Hilbert function of the Ratliff-Rush filtration.
• Depth of associated graded rings via Hilbert coefficients of ideals
• Reduction Numbers and Rees Algebras of Powers of an Ideal
• Reduction Exponent and Degree Bound for the Defining Equations of Graded Rings
• The Coefficients of the Hilbert Polynomial and the Reduction Number of an Ideal
• Hilbert Coefficients and the Depths of Associated Graded Rings
• Cohen-Macaulay Local Rings of Embedding Dimension e + d − 3

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