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Die eindeutigkeit der koordinatisierung von affinen liniengeometrien durch freie Moduln

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Abstract

If an “Affine Liniengeometrie” (see [1]) is coordinatized by a free ring-modul with dimension n, then modul and ring are uniquely determined up to isomorphism. This statement, which is proved in [1] for infinite n, will be proved for n ≠ 1.

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Literatur

  1. Arnold, H.-J., Die Geometrie der Ringe im Rahmen allgemeiner affiner Strukturen. Hamburger Mathematische Einzelschriften. Neue Folge. Heft 4. Vandenhoeck & Ruprecht. Göttingen 1971.

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  2. Kaerlein, G., Zur Isomorphie vektorieller Gruppen und affiner Liniengeometrien. Journal of Geometry 16 (1981), S. 1–4.

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  3. Sperner, E., Affine Räume mit schwacher Inzidenz und zugehörige algebraische Strukturen. Journal f. d. reine und angew. Math. 204 (1960) S. 205–215.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität-GH-Duisburg, 4100, Duisburg, Lotharstr. 65

    Raymund Schleicher

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  1. Raymund Schleicher
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Schleicher, R. Die eindeutigkeit der koordinatisierung von affinen liniengeometrien durch freie Moduln. J Geom 22, 143–148 (1984). https://doi.org/10.1007/BF01222837

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  • DOI: https://doi.org/10.1007/BF01222837

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