Document Detail

Collinearity-preserving functions between Desarguesian planes.
MedLine Citation:
PMID:  16592845     Owner:  NLM     Status:  PubMed-not-MEDLINE    
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 in which 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.
D S Carter; A Vogt
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Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  Proceedings of the National Academy of Sciences of the United States of America     Volume:  77     ISSN:  0027-8424     ISO Abbreviation:  Proc. Natl. Acad. Sci. U.S.A.     Publication Date:  1980 Jul 
Date Detail:
Created Date:  2010-06-30     Completed Date:  2010-06-30     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7505876     Medline TA:  Proc Natl Acad Sci U S A     Country:  United States    
Other Details:
Languages:  eng     Pagination:  3756-7     Citation Subset:  -    
Department of Mathematics, Oregon State University, Corvallis, Oregon 97331.
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