| Collinearity-preserving functions between Desarguesian planes. | |
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MedLine Citation:
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PMID: 16592845 Owner: NLM Status: PubMed-not-MEDLINE |
Abstract/OtherAbstract:
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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. |
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Authors:
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D S Carter; A Vogt |
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Publication Detail:
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Type: Journal Article |
Journal Detail:
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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:
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Created Date: 2010-06-30 Completed Date: 2010-06-30 Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 7505876 Medline TA: Proc Natl Acad Sci U S A Country: United States |
Other Details:
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Languages: eng Pagination: 3756-7 Citation Subset: - |
Affiliation:
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Department of Mathematics, Oregon State University, Corvallis, Oregon 97331. |
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From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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