Boundary map and overrings of half-factorial domains

Gonzalez, Nathalie ; Pellerin, Sébastien

Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005), p. 173-185 / Harvested from Biblioteca Digitale Italiana di Matematica

Abstract

We investigate factorization of elements in overrings of a half-factorial domain $A$ in relation with the behaviour of the boundary map of $A$. It turns out that a condition, called $\mathcal{C}^{\star}$, on the extension plays a central role in this study. We finally apply our results to the special case of $A+XB[X]$ polynomial rings.

Résumé

In questo articolo studiamo la fattorizzazione di elementi nei sopranelli di un dominio metà-fattoriale $A$ in funzione del comportamento della funzione di bordo di $A$. A tale riguardo, troviamo che gioca un ruolo centrale una condizione sulle estensioni, che chiamiamo condizione $\mathcal{C}^{\star}$. Quindi studiamo quando questa condizione $\mathcal{C}C^{\star}$ è verificata. Infine, applichiamo i risultati ottenuti al caso speciale degli anelli di polinomi.

Détail

Publié le : 2005-02-01

MR 2122982 | Zbl 1150.13003

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