Powers of ideals. Primary decompositions, Artin-Rees lemma and regularity

DOI10.1007/s002080050035zbMath0869.13001OpenAlexW2021412712MaRDI QIDQ1359530

Irena Swanson

Publication date: 1 September 1997

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002080050035

zbMATH Keywords

asymptotic propertiesCastelnuovo-Mumford regularityprimary decompositionpolynomial idealArtin-Rees lemma

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Ideals and multiplicative ideal theory in commutative rings (13A15)

Related Items (39)

Depth and regularity of powers of sums of ideals ⋮ LINEAR GROWTH OF PRIMARY DECOMPOSITIONS OF MODULES AND INTEGRAL CLOSURES ⋮ Minimal free resolutions and asymptotic behavior of multigraded regularity ⋮ QUADRATIC SEQUENCES AND POWERS OF IDEALS ⋮ Adjunction ofpth Roots to Dedekind Domains and Injective Modules ⋮ Homology of Powers of Ideals: Artin-Rees Numbers of Syzygies and the Golod Property ⋮ Associated points and integral closure of modules ⋮ Ideals in a perfect closure, linear growth of primary decompositions, and tight closure ⋮ Epsilon multiplicity for Noetherian graded algebras ⋮ Asymptotic multiplicities of graded families of ideals and linear series ⋮ Asymptotic linear bounds of Castelnuovo-Mumford regularity in multigraded modules ⋮ Asymptotic invariants constructed from generic initial ideals ⋮ Duality for asymptotic invariants of graded families ⋮ Frobenius methods in combinatorics ⋮ Expected resurgence of ideals defining Gorenstein rings ⋮ Ideals contracted from 1-dimensional overrings with an application to the primary decomposition of ideals ⋮ Ratliff–Rush closures and linear growth of primary decompositions of ideals ⋮ Stabilization of Betti tables ⋮ Expected resurgences and symbolic powers of ideals ⋮ Asymptotic multiplicities ⋮ Mixed multiplicities of graded families of ideals ⋮ Asymptotic behaviour of standard bases ⋮ Upper bounds for the regularity of powers of edge ideals of graphs ⋮ Uniform equivalence of symbolic and adic topologies ⋮ Primary decomposition: Compatibility, independence and linear growth ⋮ Asymptotic linear bounds for the Castelnuovo-Mumford regularity ⋮ Asymptotic behaviour of arithmetically Cohen-Macaulay blow-ups ⋮ Local Okounkov bodies and limits in prime characteristic ⋮ Epsilon multiplicity for graded algebras ⋮ Uniform symbolic topologies in abelian extensions ⋮ Growth of primary decompositions of Frobenius powers of ideals ⋮ The complexity of Frobenius powers of ideals ⋮ A vanishing theorem and asymptotic regularity of powers of ideal sheaves ⋮ Binomial Canonical Decompositions of Binomial Ideals ⋮ On the asymptotic linearity of Castelnuovo-Mumford regularity. ⋮ Chudnovsky’s conjecture and the stable Harbourne–Huneke containment ⋮ Asymptotic Hilbert polynomials and limiting shapes ⋮ The (ir)regularity of Tor and Ext ⋮ Primary decomposition. II: Primary components and linear growth

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