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Morphisms and Semilinear Maps

  • Claude-Alain Faure
  • Alfred Frölicher
Chapter
  • 579 Downloads
Part of the Mathematics and Its Applications book series (MAIA, volume 521)

Abstract

We start with the theorem that every non-degenerate morphism g: P V - - → P W is of the form g = P f for some semilinear map f : VW, where non-degenerate means that Im g contains three non-collinear points. This implies immediately the Fundamental Theorem of projective geometry: Every non-degenerate morphism g between arguesian geometries is described in homogeneous coordinates by a semi-linear map f. For given coordinates f is unique up to a non-zero constant factor. Moreover, the map f is quasilinear if and only if g is a homomorphism.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Claude-Alain Faure
    • 1
  • Alfred Frölicher
    • 1
  1. 1.University of GenevaGenevaSwitzerland

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