Reduction Numbers and Rees Algebras of Powers of an Ideal

DOI10.2307/2159922zbMath0812.13004OpenAlexW4247133720MaRDI QIDQ3142835

Lê Tuân Hoa

Publication date: 18 May 1995

Full work available at URL: https://doi.org/10.2307/2159922

zbMATH Keywords

analytic spreadlocal ringCohen-MacaulaynessRees ringreduction exponent

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Ideals and multiplicative ideal theory in commutative rings (13A15) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items (16)

When are the rings I:I Gorenstein? ⋮ Asymptotic behavior of reduction numbers ⋮ Local cohomology bounds and the weak implies strong conjecture in dimension 4 ⋮ On the asymptotic linearity of reduction number ⋮ Ratliff-Rush filtration, regularity and depth of higher associated graded modules. II. ⋮ Reduction numbers and multiplicities of multigraded structures ⋮ Generalized Hilbert-Kunz function of the Rees algebra of the face ring of a simplicial complex ⋮ Ratliff-Rush filtration, Hilbert coefficients and reduction number of integrally closed ideals ⋮ Gorensteinness in Rees algebras of powers of parameter ideals ⋮ Bounding Hilbert coefficients of parameter ideals ⋮ On the reduction numbers of monomial ideals ⋮ On the Hilbert coefficients, depth of associated graded rings and reduction numbers ⋮ Results on the Hilbert coefficients and reduction numbers ⋮ Reduction numbers of equimultiple ideals ⋮ Bounds for Hilbert coefficients ⋮ Castelnuovo-Mumford regularity and Hilbert coefficients of parameter ideals

Cites Work

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• Stable ideals in Gorenstein local rings
• Castelnuovo's regularity of graded rings and modules
• Linear free resolutions and minimal multiplicity
• Local cohomology of certain Rees- and form-rings. II
• On the canonical module of the Rees algebra and the associated graded ring of an ideal
• On graded rings. I
• Some remarks on generalized Cohen-Macaulay rings
• Stable rings
• On complete d-sequences and the defining ideals of Rees algebras
• When is the rees algebra cohen—macaulay?
• Reduction numbers for ideals of higher analytic spread
• Reduction Exponent and Degree Bound for the Defining Equations of Graded Rings
• On the Gorenstein Property of Rees and Form Rings of Power of Ideals
• Toward a theory of generalized Cohen-Macaulay modules

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