On the Depth of the Associated Graded Ring

DOI10.2307/2160603zbMath0830.13001OpenAlexW4234449122MaRDI QIDQ4318367

Anna Guerrieri

Publication date: 6 February 1996

Full work available at URL: https://doi.org/10.2307/2160603

zbMATH Keywords

Cohen-Macaulay local ringassociated graded ringdepth

Mathematics Subject Classification ID

Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15)

Related Items (5)

On the depth of the tangent cone and the growth of the Hilbert function ⋮ On the Hilbert coefficients, depth of associated graded rings and reduction numbers ⋮ On the associated graded rings of ideals of reduction number 2 ⋮ Estimates on the depth of the associated graded ring ⋮ The Valabrega–Valla module of monomial ideals

Cites Work

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• Hilbert functions and symbolic powers
• On form rings which are Cohen-Macaulay
• On the depth of the associated graded ring of an \(m\)-primary ideal of a Cohen-Macaulay local ring
• Ideals whose Hilbert function and Hilbert polynomial agree at \(n=1\)
• R-Sequences and Homological Dimension
• Reduction numbers for ideals of higher analytic spread
• Reduction Exponent and Degree Bound for the Defining Equations of Graded Rings
• Reduction numbers and Hilbert polynomials of ideals in higher dimensional CohenMacaulay local rings
• Form rings and regular sequences
• The Coefficients of the Hilbert Polynomial and the Reduction Number of an Ideal

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