Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Finite_field> ?p ?o }
- Finite_field abstract "In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod n when n is a prime number.The number of elements of a finite field is called its order. A finite field of order q exists if and only if the order q is a prime power pk (where p is a prime number and k is a positive integer). All fields of a given order are isomorphic. In a field of order pk, adding p copies of any element always results in zero; that is, the characteristic of the field is p. In a finite field of order q, the polynomial Xq − X has all q elements of the finite field as roots. The non-zero elements of a finite field form a multiplicative group. This group is cyclic, so all non-zero elements can be expressed as powers of a single element called a primitive element of the field (in general there will be several primitive elements for a given field.)A field has, by definition, a commutative multiplication operation. A more general algebraic structure that satisfies all the other axioms of a field but isn't required to have a commutative multiplication is called a division ring (or sometimes skewfield). A finite division ring is a finite field by Wedderburn's little theorem. This result shows that the finiteness condition in the definition of a finite field can have algebraic consequences.Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory.Finite fields appear in the following chain of class inclusions: Commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ finite fields".
- Finite_field wikiPageExternalLink FiniteField.html.
- Finite_field wikiPageID "11615".
- Finite_field wikiPageLength "35914".
- Finite_field wikiPageOutDegree "132".
- Finite_field wikiPageRevisionID "682645155".
- Finite_field wikiPageWikiLink Abelian_group.
- Finite_field wikiPageWikiLink Algebraic_closure.
- Finite_field wikiPageWikiLink Algebraic_geometry.
- Finite_field wikiPageWikiLink Alternative_algebra.
- Finite_field wikiPageWikiLink Alternative_ring.
- Finite_field wikiPageWikiLink Artin–Zorn_theorem.
- Finite_field wikiPageWikiLink Automorphism.
- Finite_field wikiPageWikiLink Binomial_coefficient.
- Finite_field wikiPageWikiLink Cambridge_University_Press.
- Finite_field wikiPageWikiLink Category:Finite_fields.
- Finite_field wikiPageWikiLink Characteristic_(algebra).
- Finite_field wikiPageWikiLink Chinese_remainder_theorem.
- Finite_field wikiPageWikiLink Coding_theory.
- Finite_field wikiPageWikiLink Computer_algebra_system.
- Finite_field wikiPageWikiLink Coprime.
- Finite_field wikiPageWikiLink Coprime_integers.
- Finite_field wikiPageWikiLink Cryptographic_protocol.
- Finite_field wikiPageWikiLink Cryptography.
- Finite_field wikiPageWikiLink Cyclic_group.
- Finite_field wikiPageWikiLink Cyclotomic_polynomial.
- Finite_field wikiPageWikiLink Diffie–Hellman.
- Finite_field wikiPageWikiLink Diffie–Hellman_key_exchange.
- Finite_field wikiPageWikiLink Direct_limit.
- Finite_field wikiPageWikiLink Discrete_logarithm.
- Finite_field wikiPageWikiLink Discrete_logarithm_problem.
- Finite_field wikiPageWikiLink Distinct_degree_factorization.
- Finite_field wikiPageWikiLink Division_ring.
- Finite_field wikiPageWikiLink E._H._Moore.
- Finite_field wikiPageWikiLink ECDHE.
- Finite_field wikiPageWikiLink Element_(mathematics).
- Finite_field wikiPageWikiLink Elementary_abelian_group.
- Finite_field wikiPageWikiLink Elliptic_curve.
- Finite_field wikiPageWikiLink Elliptic_curve_Diffie–Hellman.
- Finite_field wikiPageWikiLink Elliptic_curves.
- Finite_field wikiPageWikiLink Euclidean_division.
- Finite_field wikiPageWikiLink Euclidean_division_of_polynomials.
- Finite_field wikiPageWikiLink Eulers_totient_function.
- Finite_field wikiPageWikiLink Exponentiation_by_squaring.
- Finite_field wikiPageWikiLink Expression_(mathematics).
- Finite_field wikiPageWikiLink Extended_Euclidean_algorithm.
- Finite_field wikiPageWikiLink Factorization_of_polynomials.
- Finite_field wikiPageWikiLink Factorization_of_polynomials_over_finite_fields.
- Finite_field wikiPageWikiLink Ferdinand_Georg_Frobenius.
- Finite_field wikiPageWikiLink Fermats_little_theorem.
- Finite_field wikiPageWikiLink Field_(mathematics).
- Finite_field wikiPageWikiLink Field_automorphism.
- Finite_field wikiPageWikiLink Field_axioms.
- Finite_field wikiPageWikiLink Field_with_one_element.
- Finite_field wikiPageWikiLink Finite_field_arithmetic.
- Finite_field wikiPageWikiLink Finite_geometry.
- Finite_field wikiPageWikiLink Finite_group.
- Finite_field wikiPageWikiLink Finite_ring.
- Finite_field wikiPageWikiLink Formal_derivative.
- Finite_field wikiPageWikiLink Frobenius_automorphism.
- Finite_field wikiPageWikiLink Frobenius_endomorphism.
- Finite_field wikiPageWikiLink Function_composition.
- Finite_field wikiPageWikiLink Galois_extension.
- Finite_field wikiPageWikiLink Galois_theory.
- Finite_field wikiPageWikiLink Hamming_space.
- Finite_field wikiPageWikiLink Hasse_principle.
- Finite_field wikiPageWikiLink Hensel_lifting.
- Finite_field wikiPageWikiLink Hensels_lemma.
- Finite_field wikiPageWikiLink Identity_(mathematics).
- Finite_field wikiPageWikiLink Integer.
- Finite_field wikiPageWikiLink Integers_mod_n.
- Finite_field wikiPageWikiLink Irreducible_polynomial.
- Finite_field wikiPageWikiLink Isomorphic.
- Finite_field wikiPageWikiLink Isomorphism.
- Finite_field wikiPageWikiLink Krull_topology.
- Finite_field wikiPageWikiLink LLL_algorithm.
- Finite_field wikiPageWikiLink Lagranges_theorem_(group_theory).
- Finite_field wikiPageWikiLink Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm.
- Finite_field wikiPageWikiLink Linear_algebra.
- Finite_field wikiPageWikiLink Linear_map.
- Finite_field wikiPageWikiLink Linear_subspace.
- Finite_field wikiPageWikiLink Mathematics.
- Finite_field wikiPageWikiLink Modular_arithmetic.
- Finite_field wikiPageWikiLink Monic_polynomial.
- Finite_field wikiPageWikiLink Multiplicative_group.
- Finite_field wikiPageWikiLink Möbius_function.
- Finite_field wikiPageWikiLink Number_theory.
- Finite_field wikiPageWikiLink Perfect_field.
- Finite_field wikiPageWikiLink Polynomial.
- Finite_field wikiPageWikiLink Polynomial_factorization.
- Finite_field wikiPageWikiLink Polynomial_greatest_common_divisor.
- Finite_field wikiPageWikiLink Polynomial_ring.
- Finite_field wikiPageWikiLink Prime_field.
- Finite_field wikiPageWikiLink Prime_number.
- Finite_field wikiPageWikiLink Prime_power.
- Finite_field wikiPageWikiLink Primitive_element_(finite_field).
- Finite_field wikiPageWikiLink Product_topology.
- Finite_field wikiPageWikiLink Profinite_group.
- Finite_field wikiPageWikiLink Profinite_integer.
- Finite_field wikiPageWikiLink Profinite_integers.