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E. Artin, O. Schreier (1927)
Algebraische Konstruktion reeller KörperAbhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 5
D. S. Carter, A. Vogt (1980)
Collinearity preserving functions between projective Desarguesian planesMemoirs AMS, 27
W. Ledermann (1966)
Lectures in Abstract Algebra : vol. III, Theory of Fields and Galois Theory. By N. Jacobson. Pp. xi, 323. 76s. (Van Nostrand)The Mathematical Gazette, 50
D. Carter, A. Vogt (1980)
Collinearity-preserving functions between Desarguesian planes.Proceedings of the National Academy of Sciences of the United States of America, 77 7
W. Klingenberg (1956)
Projektive Geometrien mit HomomorphismusMathematische Annalen, 132
A. Brezuleanu, D. Radulescu (1984)
About full or injective lineationsJournal of Geometry, 23
N. Jacobson (1951)
Lectures In Abstract Algebra
E. Artin, O. Schreier (1927)
Algebraische Konstruktion reeller KörperAbhandlungen des Mathematischen Seminars der hamburgischen Universität, 5
F. Radó (1969)
Darstellung nicht-injektiver Kollineationen eines projektiven Raumes durch verallgemeinerte semilineare AbbildungenMathematische Zeitschrift, 110
F. Radó (1970)
Non-injective collineations on some sets in desarguesian projective planes and extension of non-commutative valuationsaequationes mathematicae, 4
H. Schaeffer (1980)
Über eine Verallgemeinerung des Fundamentalsatzes in desargues-schen affinen EbenenBeiträge zur Geometrie u. Algebra, 6
Abh. Math. Sere. Univ. Hamburg 55, 171--181 (1985) Characterizing lineations defined on open subsets of projective spaces over ordered division rings By A. BREZVL~A~U and D. C. RADVLESCV To the memory o] Iulian Popoviei 1. Introduction The source and in some sense the significance of this paper is corollary 3.2 which we proved initially for open subsets of projective spaces over ll(([2]). Comparing with the known results about lineations the most important new fact is that the domains on which the lineations are defined are allowed to be "bounded", i.e. they do not contain lines (compare with [8] and [9]). The known equivalence between projective spaces with full lineations and division rings with places (see [6], [7]) is obtained here for ordered division rings, even if the domains of the lineations are "bounded" (see 2.4). We heartily thank Prof. F. Rad6 for the suggestion to consider also non-injective lineations. We are indebted to our late friend Dr. Iulian Popovici from whom we acquired our geometric skill. Let m ~ 2 be a natural number. If T is a division ring, i.e. a (skew-) field, denote by Pro(T) the m-dimensional projective space over T, and by p(Ul .... , ur)
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Aug 28, 2008
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