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Pappus' theorem for ring-geometries - MaRDI portal

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Pappus' theorem for ring-geometries (Q1267344)

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scientific article; zbMATH DE number 1208018
Language Label Description Also known as
English
Pappus' theorem for ring-geometries
scientific article; zbMATH DE number 1208018

    Statements

    title
    Pappus' theorem for ring-geometries (English)
    0 references
    author
    Thorsten Pfeiffer
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    publication date
    4 August 1999
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    review text
    Analogously to the projective planes over fields the plane geometry over any unitary and associative ring \(R\) is studied. It can be described by the set of submodules spanned by one element within the lattice of all submodules of \(R^3\) over \(R\). By means of perspectivities for regular triangles an enhanced Pappus configuration (EP) is defined. It is shown: \(R\) is a commutative ring if and only if (EP) is fulfilled for one and with it for all regular triangles.
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    reviewed by
    Herbert Hotje
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    zbMATH Keywords
    projective ring geometry
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    Pappus' theorem
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    plane geometry
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    Identifiers

    Mathematics Subject Classification ID
    51C05
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    51A05
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    51A10
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    zbMATH DE Number
    1208018
    0 references
     
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