The Reduction Number of an Ideal and the Local Cohomology of the Associated Graded Ring

DOI10.2307/2159165zbMath0772.13006OpenAlexW4249921893MaRDI QIDQ4038365

Thomas Marley

Publication date: 16 May 1993

Full work available at URL: https://doi.org/10.2307/2159165

zbMATH Keywords

Hilbert functionlocal ringlocal cohomology modulesreduction numberCohen Macaulay ring

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Local cohomology and commutative rings (13D45)

Related Items (30)

Bounds on the \(a\)-invariant and reduction numbers of ideals ⋮ Castelnuovo-Mumford regularity and extended degree ⋮ Castelnuovo-Mumford regularity, postulation numbers, and reduction numbers ⋮ On Hilbert functions and cohomology ⋮ Ratliff-Rush filtration, regularity and depth of higher associated graded modules. I ⋮ Reduction numbers and multiplicities of multigraded structures ⋮ Multigraded regularity, reduction vectors and postulation vectors ⋮ Hilbert functions of graded algebras over Artinian rings ⋮ Castelnuovo-Mumford regularity, postulation numbers and relation types ⋮ Graded filtrations and ideals of reduction number 2 ⋮ When is \(\mathfrak{m}:\mathfrak{m}\) an almost Gorenstein ring? ⋮ Upper bounds on two Hilbert coefficients ⋮ On Hilbert-Samuel coefficients of graded local cohomology modules ⋮ On the computation of the Ratliff-Rush closure, associated graded ring and invariance of a length ⋮ On the reduction numbers of monomial ideals ⋮ Filter-regularity and cohen-macaulay multigraded rees algebras ⋮ On associated graded rings of normal ideals ⋮ Ideals generated by quadrics ⋮ A note on reduction numbers and Hilbert--Samuel functions of ideals over Cohen--Macaulay rings ⋮ On a-invariant formulas ⋮ On the Hilbert coefficients, depth of associated graded rings and reduction numbers ⋮ Ratliff–Rush ideal and reduction numbers ⋮ Hilbert coefficients and the depth of associated graded rings with respect to parameter ideals ⋮ Results on the Hilbert coefficients and reduction numbers ⋮ Reduction numbers of equimultiple ideals ⋮ Ideals of reduction number two ⋮ Graphs over graded rings and relation with Hamming graph ⋮ The Castelnuovo regularity of the Rees algebra and the associated graded ring ⋮ The largest non-vanishing degree of graded local cohomology modules ⋮ Castelnuovo-Mumford regularity and Hilbert coefficients of parameter ideals

Cites Work

• Genera and arithmetic genera of commutative rings
• On stable ideals
• On form rings which are Cohen-Macaulay
• Depth properties of Rees algebras and associated graded rings
• Reduction numbers for ideals of higher analytic spread
• Reduction Exponent and Degree Bound for the Defining Equations of Graded Rings
• Form rings and regular sequences
• The Coefficients of the Hilbert Polynomial and the Reduction Number of an Ideal
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