Geodesic
Boundary map and overrings of half-factorial domains
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 1, pp. 173-185.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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.
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. 
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Gonzalez, Nathalie; Pellerin, Sébastien. Boundary map and overrings of half-factorial domains. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 1, pp. 173-185. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_1_a9/

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