Abstract: We give give an elementary and constructive version of the theory of "Pr\"ufer v-Multiplication Domains" (which we call "anneaux \`a 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 pr\'esentons dans cet article une approche constructive, dans le style de Bishop, de la th\'eorie des diviseurs et des anneaux de Krull. Nous accordons une place centrale aux "anneaux \`a diviseur...
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Humanities
Pure mathematics