Two counterexamples about the Nagata and Serre conjecture rings

DOI10.1016/S0022-4049(99)00108-5zbMath0974.13017OpenAlexW2016438784WikidataQ123107545 ScholiaQ123107545MaRDI QIDQ1587978

Ihsen Yengui

Publication date: 6 December 2001

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-4049(99)00108-5

zbMATH Keywords

Serre conjectureNagata conjecturecancellation of polynomial rings

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials over commutative rings (13B25) Ideals and multiplicative ideal theory in commutative rings (13A15)

Related Items (5)

A question about saturated chains of primes in Serre conjecture rings ⋮ About the Spectrum of the RingsR(n) andR⟨n⟩ ⋮ Prüfer conditions in the Nagata ring and the Serre’s conjecture ring ⋮ About the spectrum of Nagata rings ⋮ On questions related to saturated chains of primes in polynomial rings

Cites Work

• Unnamed Item
• Strong S-domains
• Sur les S-domaines forts de Kaplansky. (On strong Kaplansky S-domains)
• Une conjecture sur les anneaux de Nagata. (A conjecture on Nagata rings)
• Construction B, I, D et anneaux localement ou residuellement de Jaffard. (B, I, D construction and locally or residually Jaffard rings)
• The rings R(X) and \(R<X>\)
• Couples d'anneaux partageant un idéal. (Couples of rings sharing an ideal)
• R Noetherian implies \(R\langle X\rangle\) is a Hilbert ring
• One counterexample for two open questions about the rings \(R(X)\) and \(R\langle X\rangle\)
• The Nullstellensatz and Tensor Products of Fields
• Valuative Heights and Infinite Nagata Rings

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