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arXiv · 1507.02880

Anneaux à diviseurs et anneaux de Krull (une approche constructive)

Thierry Coquand·Henri Lombardi
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Abstract

We give give an elementary and constructive version of the theory of "Prüfer v-Multiplication Domains" (which we call "anneaux à diviseurs" in the paper) and Krull Domains. The main results of these theories are revisited from a constructive point of view, following the Bishop style, and without assuming properties of complete factorizations. Nous présentons dans cet article une approche constructive, dans le style de Bishop, de la théorie des diviseurs et des anneaux de Krull. Nous accordons une place centrale aux "anneaux à diviseurs," appelés PvMD dans la littérature anglaise. Les résultats classiques sont obtenus comme résultats d'algorithmes explicites sans faire appel aux hypothèses de factorisation complète.

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Thierry Coquand, Henri Lombardi. 2024-01-04. Anneaux à diviseurs et anneaux de Krull (une approche constructive). https://doi.org/10.1080/00927872.2014.975346

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