Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Field_with_one_element> ?p ?o. }
Showing items 1 to 49 of
49
with 100 items per page.
- Field_with_one_element abstract "In mathematics, the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, if such a field could exist. This object is denoted F1, or, in a French–English pun, Fun. The name "field with one element" and the notation F1 are only suggestive, as there is no field with one element in classical abstract algebra. Instead, F1 refers to the idea that there should be a way to replace sets and operations, the traditional building blocks for abstract algebra, with other, more flexible objects. While there is still no field with a single element in these theories, there is a field-like object whose characteristic is one.F1 cannot be a field because all fields must contain two distinct elements, the additive identity zero and the multiplicative identity one. Even if this restriction is dropped, a ring with one element must be the zero ring, which does not behave like a finite field. Instead, most proposed theories of F1 replace abstract algebra entirely. Mathematical objects such as vector spaces and polynomial rings can be carried over into these new theories by mimicking their abstract properties. This allows the development of commutative algebra and algebraic geometry on new foundations. One of the defining features of theories of F1 is that these new foundations allow more objects than classical abstract algebra, one of which behaves like a field of characteristic one.The possibility of studying the mathematics of F1 was originally suggested in 1956 by Jacques Tits, published in (Tits 1957), on the basis of an analogy between symmetries in projective geometry and the combinatorics of simplicial complexes. F1 has been connected to noncommutative geometry and to a possible proof of the Riemann hypothesis. Many theories of F1 have been proposed, but it is not clear which, if any, of them give F1 all the desired properties.".
- Field_with_one_element wikiPageExternalLink Fun.
- Field_with_one_element wikiPageExternalLink 0909.0069.
- Field_with_one_element wikiPageExternalLink the_field_with_one_element.html.
- Field_with_one_element wikiPageExternalLink week259.html.
- Field_with_one_element wikiPageExternalLink ncg-and-fun.html.
- Field_with_one_element wikiPageExternalLink the-field-with-one-element.
- Field_with_one_element wikiPageExternalLink soule.
- Field_with_one_element wikiPageExternalLink schedule_workshop08.pdf.
- Field_with_one_element wikiPageExternalLink workshop2008.html.
- Field_with_one_element wikiPageExternalLink KapranovSmirnov.pdf.
- Field_with_one_element wikiPageExternalLink looking-for-f_un.html.
- Field_with_one_element wikiPageExternalLink the-f_un-folklore.html.
- Field_with_one_element wikiPageExternalLink algabsodef.pdf.
- Field_with_one_element wikiPageID "13798040".
- Field_with_one_element wikiPageRevisionID "600510291".
- Field_with_one_element b "1".
- Field_with_one_element b "q".
- Field_with_one_element hasPhotoCollection Field_with_one_element.
- Field_with_one_element p "2".
- Field_with_one_element p "n".
- Field_with_one_element subject Category:Algebraic_geometry.
- Field_with_one_element subject Category:Finite_fields.
- Field_with_one_element subject Category:Noncommutative_geometry.
- Field_with_one_element type Field108569998.
- Field_with_one_element type FiniteFields.
- Field_with_one_element type GeographicalArea108574314.
- Field_with_one_element type Location100027167.
- Field_with_one_element type Object100002684.
- Field_with_one_element type PhysicalEntity100001930.
- Field_with_one_element type Region108630985.
- Field_with_one_element type Tract108673395.
- Field_with_one_element type YagoGeoEntity.
- Field_with_one_element type YagoLegalActorGeo.
- Field_with_one_element type YagoPermanentlyLocatedEntity.
- Field_with_one_element comment "In mathematics, the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, if such a field could exist. This object is denoted F1, or, in a French–English pun, Fun. The name "field with one element" and the notation F1 are only suggestive, as there is no field with one element in classical abstract algebra.".
- Field_with_one_element label "Campo con un elemento".
- Field_with_one_element label "Corps à un élément".
- Field_with_one_element label "Field with one element".
- Field_with_one_element label "一元体".
- Field_with_one_element sameAs Corps_à_un_élément.
- Field_with_one_element sameAs Campo_con_un_elemento.
- Field_with_one_element sameAs 一元体.
- Field_with_one_element sameAs m.03cjkpx.
- Field_with_one_element sameAs Q3654641.
- Field_with_one_element sameAs Q3654641.
- Field_with_one_element sameAs Field_with_one_element.
- Field_with_one_element wasDerivedFrom Field_with_one_element?oldid=600510291.
- Field_with_one_element isPrimaryTopicOf Field_with_one_element.