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On linear spaces and matroids of arbitrary cardinality

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Abstract.

In this paper, we study linear spaces of arbitrary finite dimension on some (possibly infinite) set. We interpret linear spaces as simple matroids and study the problem of erecting some linear space of dimension n to some linear space of dimension n + 1 if possible. Several examples of some such erections are studied; in particular, one of these erections is computed within some infinite iteration process.

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Authors and Affiliations

  1. Mathematisches Seminar, Universität Kiel, Ludewig-Meyn-Strasse 4, 24098, Kiel, Germany

    Dieter Betten

  2. Fakultät für Mathematik, Technische Universität Chemnitz, ., 09107, Chemnitz, Germany

    Walter Wenzel

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  1. Dieter Betten
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  2. Walter Wenzel
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Correspondence to Dieter Betten.

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Dedicated to the memory of Gian-Carlo Rota

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Betten, D., Wenzel, W. On linear spaces and matroids of arbitrary cardinality. Algebra univers. 49, 259–288 (2003). https://doi.org/10.1007/s00012-003-1814-4

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  • DOI: https://doi.org/10.1007/s00012-003-1814-4

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