Geodesic
Ideal-theoretic characterizations of valuation and Prüfer monoids
Archivum mathematicum, Tome 40 (2004) no. 1, pp. 41-46.

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It is well known that an integral domain is a valuation domain if and only if it possesses only one finitary ideal system (Lorenzen $r$-system of finite character). We prove an analogous result for root-closed (cancellative) monoids and apply it to give several new characterizations of Prüfer (multiplication) monoids and integral domains.
Classification : 13A15, 13F05, 20M12, 20M14, 20M25
Keywords: valuation monoids; Prüfer domains 
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Halter-Koch, Franz. Ideal-theoretic characterizations of valuation and Prüfer monoids. Archivum mathematicum, Tome 40 (2004) no. 1, pp. 41-46. http://geodesic.mathdoc.fr/item/ARM_2004__40_1_a4/