Author | : David S. Carter |

File Size | : 42,5 Mb |

Publisher | : American Mathematical Soc. |

Language | : English |

Release Date | : 29 September 1980 |

ISBN | : 9780821822357 |

Pages | : 98 pages |

## Collinearity Preserving Functions between Desarguesian Planes by David S. Carter Book PDF Summary

Using concepts from valuation theory, we obtain a characterization of all collinearity-preserving functions from one affine or projective Desarguesian plane into another. The case in which the planes are projective and the range contains a quadrangle has been treated previously in the literature. Our results permit one or both planes to be affine and include cases where the range contains a triangle but no quadrangle. A key theorem is that, with the exception of certain embeddings defined on planes of order 2 and 3, every collinearity-preserving function from one affine Desarguesian plane into another can be extended to a collinearity-preserving function between enveloping projective planes.