Annali dell’Università di Ferrara

, Volume 28, Issue 1, pp 81–84 | Cite as

On a question of Anne Marie Nicolas concerning valuation rings

  • Paulo Ribenboim


In [3], Anne MarieNicolas asked the following question:

Does there exist a valuation domainA, having an ideal which cannot be generated by a countable set of elements, and such that its field of quotients has homological dimension 1?

We answer this question in the affirmative.


Linear Order Maximal Ideal Formal Power Series Ordinal Number Valuation Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Anne MarieNicolas in [3] pose la seguente domanda: esiste un dominio di valutazioneA avente un ideale che non può essere generato da un insieme numerabile di elementi e tale che il suo campo di quozienti abbia dimensione omologica 1?

Noi rispondiamo a questa domanda affermativamente.


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  1. [1]
    L. Fuchs,Partially Ordered Algebraic Systems, Pergamon Press, Oxford, 1963.MATHGoogle Scholar
  2. [2]
    I. Kaplansky,The homological dimension of a quotient field, Nagoya Math. J.,27 (1966), pp. 139–142.MATHMathSciNetGoogle Scholar
  3. [3]
    A. M. Nicolas,Gènéralisation d'un critère de Pontrjagin concernant les groupes sans torsion dénombrables à des modules sans torsion sur des anneaux de Dedekind. Conditions de rang, de type, de chaînes ascendantes, Springer Lecture Notes, no. 740 (1979), pp. 385–396.MathSciNetGoogle Scholar

Copyright information

© Università degli Studi di Ferrara 1982

Authors and Affiliations

  • Paulo Ribenboim
    • 1
  1. 1.Queen's UniversityKingstonCanada

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