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
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.