Displaying similar documents to “The cardinal and the idempotent number of various monoids of transformations on a finite chain.”

Ideal-theoretic characterizations of valuation and Prüfer monoids

Franz Halter-Koch (2004)

Archivum Mathematicum

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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.