Embedding of near-fields with real valuations into planar near-fields
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In  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.
KeywordsMapping Versus Uniform Structure Fundamental System Tion Versus Property Versus
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- N. Bourbaki, Algèbre commutative, Chap. 5 et 6. Paris 1964.Google Scholar
- W. Buchmann, Untersuchungen über nichtplanare Fastkörper, Diplomarbeit, Universität Duisburg 1981.Google Scholar
- L. Fuchs, Partially ordered algebraic systems, New York 1963.Google Scholar
- 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