Prüfer domain

A commutativePlanetmathPlanetmathPlanetmath integral domainMathworldPlanetmath R is a Prüfer domain if every finitely generatedMathworldPlanetmathPlanetmath nonzero ideal I of R is invertible.

Let RI denote the localizationMathworldPlanetmath of R at R\I. Then the following statements are equivalent:

A Prüfer domain is a Dedekind domain if and only if it is NoetherianPlanetmathPlanetmathPlanetmath.

If R is a Prüfer domain with quotient field K, then any domain S such that RSK is Prüfer.


  • 1 Thomas W. Hungerford. AlgebraPlanetmathPlanetmath. Springer-Verlag, 1974. New York, NY.
Title Prüfer domain
Canonical name PruferDomain
Date of creation 2013-03-22 13:47:34
Last modified on 2013-03-22 13:47:34
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 8
Author mathcam (2727)
Entry type Definition
Classification msc 16U10
Related topic ValuationDomain
Related topic DedekindDomain
Related topic PruferRing
Related topic InvertibleIdealsInSemiLocalRings