Rendiconti del Circolo Matematico di Palermo

, Volume 46, Issue 3, pp 439–450 | Cite as

Structure des algebres de valuation discrete

  • A. Lazraq Khlass
  • M. Oudadess


We define a topology τe, on anyC-algebra of discrete valuation, generalizing the topology of coefficientwise convergence on C[[X]] studied by G. R. Allan. We give a necessary and sufficient condition for τe to be complete and prove that the completion provides an algebra of discrete valuation. We also prove that if aC-algebra of discrete valuation is Fréchet andm-convex for τe then it is isomorphic to (C[[X]], τe) and then τe is the uniqueF-algebra topology in A. We prove that a commutative, unital Fréchet l.m.c.a. that is aC-algebra of valuation is in fact aC-algebra of discrete valuation and so is embeddable in (C[[X]], τe). Whence a result of H. Bouloussa.


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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • A. Lazraq Khlass
    • 1
  • M. Oudadess
    • 1
  1. 1.E.N.S.RabatMorocco

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