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Veblen–Young theorem

Index Veblen–Young theorem

In mathematics, the Veblen–Young theorem, proved by, 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. [1]

12 relations: Algebraic group, American Journal of Mathematics, Building (mathematics), Complemented lattice, Continuous geometry, Division ring, Jacques Tits, Non-Desarguesian plane, Princeton University Press, Principal ideal ring, Projective space, Von Neumann regular ring.

Algebraic group

In algebraic geometry, an algebraic group (or group variety) is a group that is an algebraic variety, such that the multiplication and inversion operations are given by regular maps on the variety.

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American Journal of Mathematics

The American Journal of Mathematics is a bimonthly mathematics journal published by the Johns Hopkins University Press.

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Building (mathematics)

In mathematics, a building (also Tits building, Bruhat–Tits building, named after François Bruhat and Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces.

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Complemented lattice

In the mathematical discipline of order theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element b satisfying a ∨ b.

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Continuous geometry

In mathematics, continuous geometry is an analogue of complex projective geometry introduced by, where instead of the dimension of a subspace being in a discrete set 0, 1,..., n, it can be an element of the unit interval.

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Division ring

In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible.

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Jacques Tits

Jacques Tits (born 12 August 1930 in Uccle) is a Belgium-born French mathematician who works on group theory and incidence geometry, and who introduced Tits buildings, the Tits alternative, and the Tits group.

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Non-Desarguesian plane

In mathematics, a non-Desarguesian plane, named after Girard Desargues, is a projective plane that does not satisfy Desargues' theorem, or in other words a plane that is not a Desarguesian plane.

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Princeton University Press

Princeton University Press is an independent publisher with close connections to Princeton University.

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Principal ideal ring

In mathematics, a principal right (left) ideal ring is a ring R in which every right (left) ideal is of the form xR (Rx) for some element x of R. (The right and left ideals of this form, generated by one element, are called principal ideals.) When this is satisfied for both left and right ideals, such as the case when R is a commutative ring, R can be called a principal ideal ring, or simply principal ring.

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Projective space

In mathematics, a projective space can be thought of as the set of lines through the origin of a vector space V. The cases when and are the real projective line and the real projective plane, respectively, where R denotes the field of real numbers, R2 denotes ordered pairs of real numbers, and R3 denotes ordered triplets of real numbers.

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Von Neumann regular ring

In mathematics, a von Neumann regular ring is a ring R such that for every a in R there exists an x in R such that.

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Redirects here:

Veblen's axiom, Veblen-Young theorem.

References

[1] https://en.wikipedia.org/wiki/Veblen–Young_theorem

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