Hidden constructions in abstract algebra. VI: The theorem of Maroscia and Brewer {\&} Costa

DOI10.1016/j.jpaa.2007.10.009zbMath1142.13006OpenAlexW2141880890MaRDI QIDQ2481800

Ihsen Yengui, Claude Quitté, Henri Lombardi

Publication date: 15 April 2008

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

Full work available at URL: https://doi.org/10.1016/j.jpaa.2007.10.009

zbMATH Keywords

projective modulePrüfer ringlocal-globalcoherent ringconstructivearithmetical ringBézout ringHilbert's program\(pp\)-ringQuillen-Suslinrereading principle

Mathematics Subject Classification ID

Projective and free modules and ideals in commutative rings (13C10) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Other constructive mathematics (03F65) Stability for projective modules (19A13)

Related Items (8)

The Gröbner ring conjecture in the lexicographic order case ⋮ The trailing terms ideal over a valuation domain ⋮ Noether normalization theorem and dynamical Gröbner bases over Bézout domains of Krull dimension 1 ⋮ A negative answer to a question about leading terms ideals of polynomial ideals ⋮ The Gröbner ring conjecture in one variable ⋮ The multivariate Serre conjecture ring ⋮ On the leading terms ideals of polynomial ideals over a valuation ring ⋮ Dynamical Gröbner bases over Dedekind rings

Cites Work

• Generating non-Noetherian modules constructively
• Dynamical Gröbner bases
• Linear equations over commutative rings and determinantal ideals
• Projective modules over R[\(X_ 1,\)\dots ,X//n, R a Prüfer domain]
• A course in constructive algebra
• Serre's conjecture
• Constructive rereading of Artin-Schreier theory
• Krull dimension, Nullstellensätze and dynamical evaluation
• Algorithmic theory of arithmetic rings, Prüfer rings and Dedekind rings. (Théorie algorithmique des anneaux arithmétiques, des anneaux de Prüfer et des anneaux de Dedekind.)
• Making the use of maximal ideals constructive
• Hidden constructions in abstract algebra. Krull Dimension of distributive lattices and commutative rings
• Projective modules over some non-noetherian polynomial rings
• Projective modules over polynomial rings
• Dynamical method in algebra: Effective Nullstellensätze
• Hidden constructions in abstract algebra. I: Integral dependance.
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