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Topologische Divisionsalgebren ohne zugehörige topologische affine Ebene

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Abstract

We prove that many (non-associative) topological division algebrasD of dimensionn ∈ N over the centreK do not yield topological affine or projective planes (of Lenz-Barlotti type V) in contrast to the results of SKORNJAKOV [20], SALZMANN [18] and [19], GRUNDHÖFER [7], HARTMANN [11] and RINK [17] concerning projective planes coordinatized by compact or special topological ternary fields. In particular, this holds for every non-trivial and non-archimedian valuation topology ofK distinct from the order topology ifK is a real-closed field, and if the division algebraD =K n carries the product topology.

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  1. Mathematisches Institut B, Universität Stuttgart, Pfaffenwaldring 57, W-7000, Stuttgart 80, Deutschland

    E. Eisele

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  1. E. Eisele
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Eisele, E. Topologische Divisionsalgebren ohne zugehörige topologische affine Ebene. Abh.Math.Semin.Univ.Hambg. 62, 169–177 (1992). https://doi.org/10.1007/BF02941624

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  • DOI: https://doi.org/10.1007/BF02941624

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