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Results in Mathematics

, Volume 7, Issue 1, pp 58–62 | Cite as

Embedding of near-fields with real valuations into planar near-fields

  • Detlef Gröger
Article

Abstract

In [7] Wefelscheid studied all examples of nonplanar near-fields known so far. It was shown that there exists a valuation on each of these near-fields F, such that F together with the topology induced by the valuation is a topological near-field which can be completed relative to its additive uniform structure. The completion $hat F$ of F always turned out to be planar. The aim of the note presented here is to generalize these results to a class of near-fields which contains the examples mentioned above.

Keywords

Mapping Versus Uniform Structure Fundamental System Tion Versus Property Versus 
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.

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References

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    N. Bourbaki, Algèbre commutative, Chap. 5 et 6. Paris 1964.Google Scholar
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    W. Buchmann, Untersuchungen über nichtplanare Fastkörper, Diplomarbeit, Universität Duisburg 1981.Google Scholar
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    H. Wähling, Bericht über Fastkörper, Jahresber. Deutsch. Math. Verein. 76 (1974), 41–103.MATHGoogle Scholar
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    H. Wefelscheid, Vervollständigung topologischer Fastkörper, Math. Z. 99 (1967), 279–298.MathSciNetMATHCrossRefGoogle Scholar
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    H. Wefelscheid, Bewertung und Topologie in Fastkörpem, Abh. Math. Sem. Univ. Hamburg 39 (1973), 130–146.MathSciNetMATHCrossRefGoogle Scholar
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    H. Wefelscheid, Sulla immersione di quasi-corpi nonplanari in quasi-corpi planari, Proceedings Conference on Near-rings and Near-fields, San Benedetto del Tronto (Italy) 1981, 219–224.Google Scholar

Copyright information

© Birkhäuser Verlag, Basel 1984

Authors and Affiliations

  • Detlef Gröger
    • 1
  1. 1.Institut für Mathematik der TechnischenUniversität MünchenMünchen 2

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