A non-standard proof of the Briançon-Skoda theorem

DOI10.1090/S0002-9939-02-06556-5zbMath1005.13007MaRDI QIDQ3151185

Hans Schoutens

Publication date: 7 October 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

characteristic \(p\)tight closureBriançon-Skoda theoremultraproductsconvergent power series

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Non-Archimedean function theory (30G06) Formal power series rings (13F25) Power series rings (13J05) Ultraproducts and field theory (12L10)

Related Items (6)

An elementary proof of the Briançon-Skoda theorem ⋮ Dimension and singularity theory for local rings of finite embedding dimension ⋮ Lefschetz extensions, tight closure and big Cohen-Macaulay algebras ⋮ Pure subrings of regular rings are pseudo-rational ⋮ Log-terminal singularities and vanishing theorems via non-standard tight closure ⋮ LEFSCHETZ PRINCIPLE APPLIED TO SYMBOLIC POWERS

Cites Work

• Ultraproducts and approximation in local rings. I
• Jacobian ideals and a theorem of Briancon-Skoda
• Pseudo-rational local rings and a theorem of Briancon-Skoda about integral closures of ideals
• On the solutions of analytic equations
• Algebraic approximation of structures over complete local rings
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