Integrally Closed Ideals and Rees Valuation

DOI10.1080/00927872.2011.589420zbMath1262.13005OpenAlexW1969947758MaRDI QIDQ3145442

Mee-Kyoung Kim, William J. Heinzer

Publication date: 20 December 2012

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

Full work available at URL: https://doi.org/10.1080/00927872.2011.589420

zbMATH Keywords

regular local ringRees valuationminimal multiplicitynormal domainIntegrally closed ideal

Mathematics Subject Classification ID

Multiplicity theory and related topics (13H15) Commutative Noetherian rings and modules (13E05) Structure, classification theorems for modules and ideals in commutative rings (13C05) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items (2)

Finitely supported \(\ast\)-simple complete ideals and multiplicities in a regular local ring ⋮ Integrally closed ideals in regular local rings of dimension two

Cites Work

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• First neighborhood complete ideals in two-dimensional Muhly local domains
• Birational extensions in dimension two and integrally closed ideals
• Pseudo-rational local rings and a theorem of Briancon-Skoda about integral closures of ideals
• Rational singularities, with applications to algebraic surfaces and unique factorization
• Form rings and regular sequences
• On a Theorem of B. Teissier on Multiplicities of Ideals in Local Rings
• Product of distinct simple integrally closed ideals in 2-dimensional regular local rings
• Factorization of an integrally closed ideal in two-dimensional regular local rings
• A Note on Analytically Unramified Local Rings

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