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Characterizing lineations defined on open subsets of projective spaces over ordered division rings

Characterizing lineations defined on open subsets of projective spaces over ordered division rings 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) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

Characterizing lineations defined on open subsets of projective spaces over ordered division rings

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References (11)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Mathematics, general; Algebra; Differential Geometry; Number Theory; Topology; Geometry
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/BF02941495
Publisher site
See Article on Publisher Site

Abstract

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)

Journal

Abhandlungen aus dem Mathematischen Seminar der Universität HamburgSpringer Journals

Published: Aug 28, 2008

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