Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Field_with_one_element> ?p ?o }
- 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 f1-soule.pdf.
- Field_with_one_element wikiPageExternalLink KapranovSmirnov.pdf.
- Field_with_one_element wikiPageExternalLink algabsodef.pdf.
- 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 looking-for-f_un.
- Field_with_one_element wikiPageExternalLink the-f_un-folklore.
- Field_with_one_element wikiPageID "13798040".
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- Field_with_one_element wikiPageOutDegree "87".
- Field_with_one_element wikiPageRevisionID "677226953".
- Field_with_one_element wikiPageWikiLink 1_(number).
- Field_with_one_element wikiPageWikiLink Abc_conjecture.
- Field_with_one_element wikiPageWikiLink Abstract_algebra.
- Field_with_one_element wikiPageWikiLink Abstract_simplicial_complex.
- Field_with_one_element wikiPageWikiLink Additive_identity.
- Field_with_one_element wikiPageWikiLink Affine_scheme.
- Field_with_one_element wikiPageWikiLink Affine_space.
- Field_with_one_element wikiPageWikiLink Alain_Connes.
- Field_with_one_element wikiPageWikiLink Algebraic_geometry.
- Field_with_one_element wikiPageWikiLink Algebraic_group.
- Field_with_one_element wikiPageWikiLink Algebraic_number.
- Field_with_one_element wikiPageWikiLink Algebraic_number_theory.
- Field_with_one_element wikiPageWikiLink Arakelov_geometry.
- Field_with_one_element wikiPageWikiLink Arakelov_theory.
- Field_with_one_element wikiPageWikiLink Arithmetic_derivative.
- Field_with_one_element wikiPageWikiLink Binomial_coefficient.
- Field_with_one_element wikiPageWikiLink Building_(mathematics).
- Field_with_one_element wikiPageWikiLink Category:Algebraic_geometry.
- Field_with_one_element wikiPageWikiLink Category:Finite_fields.
- Field_with_one_element wikiPageWikiLink Category:Noncommutative_geometry.
- Field_with_one_element wikiPageWikiLink Characteristic_(algebra).
- Field_with_one_element wikiPageWikiLink Commutative_algebra.
- Field_with_one_element wikiPageWikiLink Complex_geometry.
- Field_with_one_element wikiPageWikiLink Cyclic_group.
- Field_with_one_element wikiPageWikiLink Degeneracy_(mathematics).
- Field_with_one_element wikiPageWikiLink Descent_(category_theory).
- Field_with_one_element wikiPageWikiLink Descent_(mathematics).
- Field_with_one_element wikiPageWikiLink Diophantine_equation.
- Field_with_one_element wikiPageWikiLink Diophantine_equations.
- Field_with_one_element wikiPageWikiLink Discrete_Fourier_transform.
- Field_with_one_element wikiPageWikiLink Discrete_Fourier_transform_(general).
- Field_with_one_element wikiPageWikiLink Dynkin_diagram.
- Field_with_one_element wikiPageWikiLink Field_extension.
- Field_with_one_element wikiPageWikiLink Filtration_(mathematics).
- Field_with_one_element wikiPageWikiLink Finite_field.
- Field_with_one_element wikiPageWikiLink Finite_set.
- Field_with_one_element wikiPageWikiLink Flag_(linear_algebra).
- Field_with_one_element wikiPageWikiLink Grassmannian.
- Field_with_one_element wikiPageWikiLink Group_Hopf_algebra.
- Field_with_one_element wikiPageWikiLink Group_action.
- Field_with_one_element wikiPageWikiLink Group_scheme_of_roots_of_unity.
- Field_with_one_element wikiPageWikiLink Homotopy_groups_of_spheres.
- Field_with_one_element wikiPageWikiLink Hopf_algebra.
- Field_with_one_element wikiPageWikiLink Institute_of_Combinatorics_and_its_Applications.
- Field_with_one_element wikiPageWikiLink Jacques_Tits.
- Field_with_one_element wikiPageWikiLink John_Baez.
- Field_with_one_element wikiPageWikiLink John_C._Baez.
- Field_with_one_element wikiPageWikiLink K-theory.
- Field_with_one_element wikiPageWikiLink Krull_dimension.
- Field_with_one_element wikiPageWikiLink Local_zeta-function.
- Field_with_one_element wikiPageWikiLink Mathematics.
- Field_with_one_element wikiPageWikiLink Matilde_Marcolli.
- Field_with_one_element wikiPageWikiLink Monad_(category_theory).
- Field_with_one_element wikiPageWikiLink Multiplicative_group.
- Field_with_one_element wikiPageWikiLink Multiplicative_identity.
- Field_with_one_element wikiPageWikiLink Nikolai_Durov.
- Field_with_one_element wikiPageWikiLink Noncommutative_geometry.
- Field_with_one_element wikiPageWikiLink Number-theoretic_transform.
- Field_with_one_element wikiPageWikiLink Pointed_set.
- Field_with_one_element wikiPageWikiLink Polynomial_ring.
- Field_with_one_element wikiPageWikiLink Primitive_root_of_unity.
- Field_with_one_element wikiPageWikiLink Projective_geometry.
- Field_with_one_element wikiPageWikiLink Projective_space.
- Field_with_one_element wikiPageWikiLink Q-Pochhammer_symbol.
- Field_with_one_element wikiPageWikiLink Q-bracket.
- Field_with_one_element wikiPageWikiLink Q-factorial.
- Field_with_one_element wikiPageWikiLink Quantum_group.
- Field_with_one_element wikiPageWikiLink Real_number.
- Field_with_one_element wikiPageWikiLink Riemann_hypothesis.
- Field_with_one_element wikiPageWikiLink Riemann_hypothesis_for_curves_over_finite_fields.
- Field_with_one_element wikiPageWikiLink Riemann_zeta_function.
- Field_with_one_element wikiPageWikiLink Riemann–Hurwitz_formula.
- Field_with_one_element wikiPageWikiLink Root_of_unity.
- Field_with_one_element wikiPageWikiLink Roots_of_unity.
- Field_with_one_element wikiPageWikiLink Schubert_cell.
- Field_with_one_element wikiPageWikiLink Schubert_variety.
- Field_with_one_element wikiPageWikiLink Semigroup_with_one_element.
- Field_with_one_element wikiPageWikiLink Set_(mathematics).
- Field_with_one_element wikiPageWikiLink Simplicial_complex.
- Field_with_one_element wikiPageWikiLink Spectrum_of_a_ring.
- Field_with_one_element wikiPageWikiLink Sphere_spectrum.