ideal inverting in Prüfer ring

Theorem.  Let  𝔞1, …, 𝔞n  be invertiblePlanetmathPlanetmathPlanetmathPlanetmath fractional ideals of a Prüfer ring.  Then also their sum and intersectionMathworldPlanetmath are invertible, and the inverse ideals of these are obtained by the formulae resembling de Morgan’s laws:


This is due to the fact, that the sum of any ideals is the smallest ideal containing these ideals and the intersection of the ideals is the largest ideal contained in each of these ideals.  Cf. sum of ideals,  quotient of ideals.


  • 1 J. Pahikkala:  “Some formulae for multiplying and inverting ideals”. - Annales universitatis turkuensis 183.  Turun yliopisto (University of Turku) 1982.
Title ideal inverting in Prüfer ring
Canonical name IdealInvertingInPruferRing
Date of creation 2015-05-06 14:34:48
Last modified on 2015-05-06 14:34:48
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 15
Author pahio (2872)
Entry type Theorem
Classification msc 13C13
Related topic DualityInMathematics
Related topic DualityOfGudermannianAndItsInverseFunction