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Periodica Mathematica Hungarica

, Volume 31, Issue 2, pp 85–96 | Cite as

Aur la vacuité du spectre d'un élément d'une algèbre\(\mathcal{L}\mathcal{F}\)

  • M. Akkar
  • C. Nacir
Article

Abstract

We give an example of a complete commutative unitary and semi-simple topological algebra, which is a locally convex inductive limit of an increasing sequence of Fréchet algebras (\(\mathcal{L}\mathcal{F}\) algebra), and which contains the field ℂ(X) of rational functions; so it contains elements which have empty spectrum and therefore does not contain any character, neither continuous nor non-continuous. This unitary algebra is not a division algebra, so it contains at least one non-trivial maximal ideal; but none of its maximal ideals is closed and they all have infinite codimension. The Gelfand-Mazur Theorem remains therefore unknown for\(\mathcal{L}\mathcal{F}\) algebras.

Mathematics subject classification numbers

1991. Primary 46J15 46J20 Secondary 30E99 

Key words and phrases

Vacuité spectre algèbre\(\mathcal{L}\mathcal{F}\) charactère d'une algèbre propriété de Gelfand-Mazur 

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Copyright information

© Akadémiai Kiadó 1995

Authors and Affiliations

  • M. Akkar
    • 1
    • 2
  • C. Nacir
    • 1
    • 2
  1. 1.Bordeux
  2. 2.UFR DE Math. Info.Université de Bordeaux ITalence CedexFrance

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