CONSTRUCTIVE KRULL DIMENSION I: INTEGRAL EXTENSIONS

DOI10.1142/S0219498809003199zbMath1172.13007OpenAlexW1965813349MaRDI QIDQ3622765

Thierry Coquand, Henri Lombardi, Lionel Ducos, Claude Quitté

Publication date: 28 April 2009

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498809003199

zbMATH Keywords

constructive mathematicsKrull dimensioncomplementary sequencesintegral extensionsCohen-Seidenberg prime extension theoremiterated boundary idealiterated boundary monoidRichman boundary ideal

Mathematics Subject Classification ID

Commutative Noetherian rings and modules (13E05) Ideals and multiplicative ideal theory in commutative rings (13A15) Other constructive mathematics (03F65) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15)

Related Items (8)

Spectral schemes as ringed lattices ⋮ Curves and coherent Prüfer rings ⋮ Krull dimension and monomial orders ⋮ On the dimensions of graded rings ⋮ A constructive theory of minimal zero-dimensional extensions ⋮ On the Krull dimension of noetherian rings ⋮ Polynômes à Valeurs Entières: Un Anneau de Prüfer de Dimension 2 ⋮ Syntax for Semantics: Krull’s Maximal Ideal Theorem

Cites Work

• Generating non-Noetherian modules constructively
• Dimension of Boolean valued lattices and rings
• A course in constructive algebra
• On a theorem of Kronecker about algebraic varieties
• Krull dimension, Nullstellensätze and dynamical evaluation
• Lifting chains of prime ideals
• A nilregular element property
• Unimodular vectors and systems generators. (Vecteurs unimodulaires et systèmes générateurs)
• A Short Proof for the Krull Dimension of a Polynomial Ring

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