Multiplicity and tight closures of parameters

DOI10.1006/jabr.2001.8907zbMath1063.13019OpenAlexW2005832501MaRDI QIDQ5952290

Yukio Nakamura, Shiro Goto

Publication date: 2001

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2001.8907

zbMATH Keywords

multiplicitytight closureCohen-MacaulaynessF-rational ringparameter ideal

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Multiplicity theory and related topics (13H15) Integral closure of commutative rings and ideals (13B22) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

Related Items (23)

A Buchsbaum theory for tight closure ⋮ On Hilbert coefficients of parameter ideals and Cohen-Macaulayness ⋮ On rings with small Hilbert-Kunz multiplicity ⋮ $F$-singularities: applications of characteristic $p$ methods to singularity theory ⋮ Chern coefficients and Cohen-Macaulay rings ⋮ The eventual index of reducibility of parameter ideals and the sequentially Cohen-Macaulay property ⋮ Tight Hilbert polynomial and F-rational local rings ⋮ On lower bounds for \(s\)-multiplicities ⋮ On Hilbert coefficients and sequentially generalized Cohen–Macaulay modules ⋮ Index of reducibility of parameter ideals and Cohen-Macaulay rings ⋮ Gorensteinness in Rees algebras of powers of parameter ideals ⋮ On the sectional genera and Cohen-Macaulay rings ⋮ Hilbert coefficients and sequentially Cohen-Macaulay modules ⋮ The first Euler characteristics versus the homological degrees ⋮ On the index of reducibility of parameter ideals: the stable and limit values ⋮ The second Hilbert coefficients and the homological torsions of parameters ⋮ The bound of the difference between parameter ideals and their tight closures. ⋮ Hilbert-Kunz Multiplicity of Three-Dimensional Local Rings ⋮ On adjusted Hilbert-Samuel functions ⋮ Colength, multiplicity, and ideal closure operations ⋮ New estimates of Hilbert–Kunz multiplicities for local rings of fixed dimension ⋮ The Chern numbers and Euler characteristics of modules ⋮ Lower bounds on Hilbert–Kunz multiplicities and maximal F-signatures

Cites Work

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• Hilbert-Kunz multiplicity and an inequality between multiplicity and colength
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• Verallgemeinerte COHEN-MACAULAY-Moduln

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