Constructions cach\'ees en alg\`ebre abstraite. Dimension de Krull, Going Up, Going Down (revised version, 2008)
Thierry Coquand, Henri Lombardi

TL;DR
This paper develops constructive versions of Krull's dimension theory for rings and lattices, enabling explicit computation and a partial realization of Hilbert's program in classical algebra.
Contribution
It introduces constructive approaches to classical theorems in Krull dimension theory, allowing explicit computation and applications to concrete objects.
Findings
Constructive versions of Krull's dimension theory for rings and lattices.
Explicit computational content derived from classical theorems.
Application to a partial realization of Hilbert's program in algebra.
Abstract
Nous rappelons des versions constructives de la th\'eorie de la dimension de Krull dans les anneaux commutatifs et dans les treillis distributifs, dont les bases ont \'et\'e pos\'ees par Joyal, Espan\~ol et les deux auteurs. Nous montrons sur les exemples de la dimension des alg\`ebres de pr\'esentation finie, du Going Up, du Going Down \ldots que cela nous permet de donner une version constructive de grands th\'eor\`emes classiques, et par cons\'equent de r\'ecup\'erer un contenu calculatoire explicite lorsque ces th\'eor\`emes abstraits sont utilis\'es pour d\'emontrer l'existence d'objets concrets. Nous pensons ainsi mettre en oeuvre une r\'ealisation partielle du programme de Hilbert pour l'alg\`ebre abstraite classique. We present constructive versions of Krull's dimension theory for commutative rings and distributive lattices. The foundations of these constructive versions are…
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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras · Advanced Algebra and Logic
