In mathematics, the Veblen–Young theorem, proved by Oswald Veblen and John Wesley Young , states that a projective space of dimension at least 3 can be constructed as the projective space associated to a vector space over a division ring. Non-Desarguesian planes 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. Jacques Tits generalized the Veblen–Young theorem to Tits buildings, showing that those of rank at least 3 arise from algebraic groups.
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| - In mathematics, the Veblen–Young theorem, proved by Oswald Veblen and John Wesley Young , states that a projective space of dimension at least 3 can be constructed as the projective space associated to a vector space over a division ring. Non-Desarguesian planes 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. Jacques Tits generalized the Veblen–Young theorem to Tits buildings, showing that those of rank at least 3 arise from algebraic groups. (en)
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| - John (en)
- Oswald (en)
- John Wesley (en)
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| - Young (en)
- von Neumann (en)
- Veblen (en)
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| - In mathematics, the Veblen–Young theorem, proved by Oswald Veblen and John Wesley Young , states that a projective space of dimension at least 3 can be constructed as the projective space associated to a vector space over a division ring. Non-Desarguesian planes 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. Jacques Tits generalized the Veblen–Young theorem to Tits buildings, showing that those of rank at least 3 arise from algebraic groups. John von Neumann generalized the Veblen–Young theorem to continuous geometry, showing that a complemented modular lattice of order at least 4 is isomorphic to the principal right ideals of a von Neumann regular ring. (en)
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