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.
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References
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Gröger, D. Embedding of near-fields with real valuations into planar near-fields. Results. Math. 7, 58–62 (1984). https://doi.org/10.1007/BF03322488
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DOI: https://doi.org/10.1007/BF03322488