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.
@article{107889,
author = {Franz Halter-Koch},
title = {Ideal-theoretic characterizations of valuation and Pr\"ufer monoids},
journal = {Archivum Mathematicum},
volume = {040},
year = {2004},
pages = {41-46},
zbl = {1114.20041},
mrnumber = {2054871},
language = {en},
url = {http://dml.mathdoc.fr/item/107889}
}
Halter-Koch, Franz. Ideal-theoretic characterizations of valuation and Prüfer monoids. Archivum Mathematicum, Tome 040 (2004) pp. 41-46. http://gdmltest.u-ga.fr/item/107889/
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