E-mail. franz.halterkoch@uni-graz.at
Abstract.
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 Pr\"ufer (multiplication)
monoids and integral domains.
AMSclassification. Primary: 20M14; Secondary: 13A15.
Keywords. Valuation monoids, Pr\"{u}fer domains.