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The Veblen–Young theorem states that if the dimension of a projective space is at least 3 (meaning that there are two non-intersecting lines) then the projective space is isomorphic with the projective space of lines in a vector space over some
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give examples of 2-dimensional projective spaces that do not arise from vector spaces over division rings, showing that the restriction to dimension at least 3 is necessary.
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of dimension at least 3 can be constructed as the projective space associated to a vector space over a
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152:are distinct points and the lines through
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60:generalized the Veblen–Young theorem to
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341:, Princeton Landmarks in Mathematics,
171:Any line has at least 3 points on it.
160:meet, then so do the lines through
109:can be defined abstractly as a set
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377:Theorems in projective geometry
227:American Journal of Mathematics
382:Theorems in algebraic geometry
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307:Projective geometry Volume II
304:; Young, John Wesley (1917),
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276:Projective geometry Volume I
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84:complemented modular lattice
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196:Projective and polar spaces
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343:Princeton University Press
193:Cameron, Peter J. (1992),
125:Each two distinct points
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279:, Ginn and Co., Boston,
133:are in exactly one line.
92:von Neumann regular ring
52:Non-Desarguesian planes
88:principal right ideals
72:John von Neumann
18:Veblen–Young theorem
16:In mathematics, the
338:Continuous geometry
136:Veblen's axiom: If
80:continuous geometry
352:978-0-691-05893-1
333:von Neumann, John
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286:978-1-4181-8285-4
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22:Oswald Veblen
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371:Categories
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335:(1998) ,
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