A formula for the core of an ideal

2004/10/14 by Claudia Polini, Bernd Ulrich · 4 citations
Computer Science · Mathematics · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC #math.AG #msc:13A30 #msc:13B21 #msc:13B22 #msc:13C40 #msc:13H10

paper · pdf · doi:10.1007/s00208-004-0560-z

to appear in Math. Ann

arxiv created 2004/10/14 · openalex publication_date 2005/01/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The core of an ideal is the intersection of all its reductions. For large classes of ideals I we explicitly describe the core as a colon ideal of a power of a single reduction and a power of I.

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• Cohen-Macaulay residual intersections and their Castelnuovo-Mumford\n Regularity
• Nakayama closures, interior operations, and core-hull duality
• A characterization of two-dimensional rational singularities via Core of ideals
• Reduction Numbers and Balanced Ideals

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