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

DOI10.1016/j.jpaa.2005.12.004zbMath1106.13003arXivmath/0411324OpenAlexW3147809439MaRDI QIDQ856342

Tony Joseph Puthenpurakal

Publication date: 7 December 2006

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

Full work available at URL: https://arxiv.org/abs/math/0411324

zbMATH Keywords

associated graded ringRees algebralocal cohomologygeneralized Cohen-Macaulay moduleRatliff-Rush filtrationextended Rees ringideal of definitionsuperficial sequences

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 (22)

Ratliff-Rush filtrations associated with ideals and modules over a Noetherian ring ⋮ Castelnuovo-Mumford regularity and Ratliff-Rush closure ⋮ Ratliff-Rush filtration, regularity and depth of higher associated graded modules. II. ⋮ Bass and Betti numbers of \(A/I^n\) ⋮ Bounds for the reduction number of primary ideal in dimension three ⋮ Ratliff-Rush filtration, Hilbert coefficients and reduction number of integrally closed ideals ⋮ RELATIVE HILBERT CO-EFFICIENTS ⋮ On the computation of the Ratliff-Rush closure, associated graded ring and invariance of a length ⋮ The strong Rees property of powers of the maximal ideal and Takahashi-Dao's question ⋮ Hilbert polynomials and powers of ideals ⋮ Generalized Hilbert Functions ⋮ Growth of Hilbert coefficients of syzygy modules ⋮ Bockstein cohomology of associated graded rings ⋮ Asymptotic associate primes ⋮ Ratliff–Rush ideal and reduction numbers ⋮ Results on the Hilbert coefficients and reduction numbers ⋮ On the degree of Hilbert polynomials of derived functors ⋮ Bounds for Hilbert coefficients ⋮ On asymptotic depth of integral closure filtration and an application ⋮ A sub-functor for Ext and Cohen-Macaulay associated graded modules with bounded multiplicity ⋮ Cohen-Macaulay local rings with \(e_2 = e_1 - e + 1\) ⋮ On coefficient ideals

Uses Software

• CoCoA

Cites Work

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• Coefficients of normal Hilbert polynomials
• Super-regular sequences
• On Hilbert functions and cohomology
• Hilbert coefficients of a Cohen-Macaulay module.
• Ratliff-Rush closures of ideals with respect to a noetherian module
• Hilbert coefficients of integrally closed ideals
• On associated graded rings of normal ideals
• The Reduction Number of an Ideal and the Local Cohomology of the Associated Graded Ring
• The Castelnuovo regularity of the Rees algebra and the associated graded ring
• Normal ideals in regular rings
• Depth formulas for certain graded rings associated to an ideal
• Local Cohomology of Rees Algebras and Hilbert Functions
• Hilbert Coefficients and the Depths of Associated Graded Rings
• DEPTH OF HIGHER ASSOCIATED GRADED RINGS
• Reduction numbers of equimultiple ideals

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