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Über eine Klasse verallgemeinerter affiner Räume

On a class of generalized affine spaces

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Abstract

The geometries associated with uncomplete nearfields (pseudoaffine spaces) are considered. The properties concerning incidence and the existence of a sharply transitive group of translations in pseudoaffine spaces give rise to the introduction of a new class of incidence structures (pseudotranslationstructures). In analogy to the equivalence between translationstructures and partitions of groups a canonical correspondence between pseudotranslationstructures with distinguished points and “pseudopartitions of groups” is established. Necessary conditions for a pseudopartition to result from the geometry associated with an uncomplete nearfield and examples of pseudotranslationstructures which can't be deduced from such geometries are given.

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Authors and Affiliations

  1. Viktoriarain 11, CH-3013, Bern, Schweiz

    Otto Bachmann

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  1. Otto Bachmann
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Bachmann, O. Über eine Klasse verallgemeinerter affiner Räume. Monatshefte für Mathematik 79, 285–297 (1975). https://doi.org/10.1007/BF01647329

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  • DOI: https://doi.org/10.1007/BF01647329

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