About: Veblen–Young theorem

An Entity of Type: Abstraction100002137, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

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.

Property Value
dbo:abstract
  • 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)
dbo:wikiPageExternalLink
dbo:wikiPageID
  • 31979549 (xsd:integer)
dbo:wikiPageLength
  • 3489 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1019240175 (xsd:integer)
dbo:wikiPageWikiLink
dbp:author1Link
  • Oswald Veblen (en)
dbp:author2Link
  • John Wesley Young (en)
dbp:authorlink
  • John von Neumann (en)
dbp:first
  • John (en)
  • Oswald (en)
  • John Wesley (en)
dbp:last
  • Young (en)
  • von Neumann (en)
  • Veblen (en)
dbp:wikiPageUsesTemplate
dbp:year
  • 1908 (xsd:integer)
  • 1910 (xsd:integer)
  • 1917 (xsd:integer)
  • 1998 (xsd:integer)
dcterms:subject
gold:hypernym
rdf:type
rdfs:comment
  • 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)
rdfs:label
  • Veblen–Young theorem (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:knownFor of
is dbo:wikiPageRedirects of
is dbo:wikiPageWikiLink of
is dbp:knownFor of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License