Archiv der Mathematik

, Volume 69, Issue 6, pp 470–478 | Cite as

Asymptotic closure of filtrations on rings with Krull dimension 1

  • Henri Dichi
  • Daouda Sangaré


In the present paper, the concept of asymptotic closure \(\overline {(f,M)}\) of a filtration f relative to a module M is introduced and investigated. The methods used by the authors in previous notes on integral and prüferian closure operations of a filtration have proved to be efficient here, despite the complexity of the asymptotic closure operation comparatively to the integral and prüferian closure operation. Our main result gives a complete description of the asymptotic closure \(\bar f\) of a filtration f on a Dedekind ring A, in terms of the prime ideals of which \(\sqrt f\) is the product, when f belongs to some class containing noetherian filtrations.


Prime Ideal Previous Note Closure Operation Dedekind Ring Asymptotic Closure 
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Copyright information

© Birkhäuser Verlag, Basel 1997

Authors and Affiliations

  • Henri Dichi
    • 1
  • Daouda Sangaré
    • 2
  1. 1.Université Blaise Pascal, Laboratoire de Mathématiques pures, Complexe des Cézeaux, F-63177 Aubiére, FranceFR
  2. 2.I.U.F.M. Centre local de Bourg en Bresse, 40 rue du général Delestraint, BP 153, F-01004 Bourg en Bresse, FranceFR

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