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An inequality involving tight closure and parameter ideals

2003/06/24 by Cătălin Ciupercă, Catalin Ciuperca, Ciuperca, Catalin +2
Mathematics · #13A35 #13D40 #13H15 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #Rings, Modules, and Algebras #math.AC #msc:13A35 #msc:13D40 #msc:13H15

paper · pdf · doi:10.48550/arxiv.math/0306349

8 pages, to appear in Bull. London Math. Soc

arxiv created 2003/06/24 · openalex publication_date 2003/06/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish an inequality involving colengths of the tight closure of ideals of systems of parameters in local rings with some mild conditions. As an application, we prove and refine a result by Goto and Nakamura, conjectured by Watanabe and Yoshida, which states that the Hilbert-Samuel multiplicity of a parameter ideal is greater than or equal to the colength of the tight closure of the ideal.

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