About: Algebraic number field

Property	Value
dbo:description	Sebuah derajat terhingga (dan karenanya aljabar) bidang ekstensi dari lapangan bilangan rasional (in) Erweiterung der rationalen Zahlen (de) Extension de corps du corps usuel des rationnels (fr) ул Q рациональ һандар яланының сикле (һәм шуға күрә — алгебраик) киңәйеүе. (ba) a finite degree (and hence algebraic) field extension of the field of rational numbers (en) rozszerzenie ciała liczb wymiernych mające skończony stopień (pl) uma extensão de corpo de grau finito (e portanto algébrica) do corpo dos números racionais (pt) extensió en un grau finit del cos de nombre racionals (ca) 有理數場嘅有限擴張 (yue) 유리수체의 유한 확대 (ko)
dbo:thumbnail	wiki-commons:Special:FilePath/Schematic_depiction_of_ramification.svg?width=300
dbo:wikiPageExternalLink	http://www.math.uconn.edu/~kconrad/blurbs/gradnumthy/unittheorem.pdf
dbo:wikiPageWikiLink	dbr:Fiber_(mathematics) dbr:Local_field dbr:Local_class_field_theory dbr:Algebraic_number_theory dbr:Group_cohomology dbr:Kronecker–Weber_theorem dbr:Eisenstein_integer dbr:Minkowski's_theorem dbr:Hilbert_class_field dbr:Ostrowski's_theorem dbr:Geometry_of_numbers dbr:Integrally_closed_domain dbr:Monogenic_field dbr:Class_number_(number_theory) dbr:Simple_pole dbr:Mathematics dbr:Going_up_and_going_down dbr:Algebraic_extension dbr:Dirichlet's_theorem_on_arithmetic_progressions dbr:Spectrum_of_a_ring dbr:Dedekind_zeta_function dbc:Field_(mathematics) dbr:Abstract_algebra dbr:Geometry dbr:Intermediate_value_theorem dbr:Richard_Dedekind dbr:Topology dbr:Algebraic_geometry dbr:Abelian_extension dbr:Scalar_multiplication dbr:Vector_space dbr:Abelianization dbr:Trace_(linear_algebra) dbr:Bilinear_form dbr:Zero_divisor dbr:Finitely_generated_module dbr:Residue_field dbr:Algebraic_K-theory dbr:American_Mathematical_Society dbr:Complex_number dbr:Real_number dbr:Addition dbr:Linear_combination dbr:Cayley–Hamilton_theorem dbr:Serge_Lang dbr:Absolute_value dbr:Algebraic_number dbr:Arithmetic_progression dbr:Ring_(mathematics) dbr:Prime_ideal dbr:Class_field_theory dbr:Sheaf_(mathematics) dbr:Analytic_continuation dbr:Division_algebra dbr:Linear_function dbr:Krull_dimension dbr:Integer_matrix dbr:Computer_algebra_system dbr:Iwasawa_theory dbr:Gaussian_integer dbr:Quadratic_integer dbr:Integral_domain dbr:Quadratic_field dbr:Euclidean_domain dbr:Local_analysis dbr:Ideal_class_group dbr:Multiplication dbr:Polynomial dbr:Set_(mathematics) dbr:André_Weil dbr:Chebotarev's_density_theorem dbr:Functional_equation dbr:Determinant dbr:Cauchy_sequence dbr:Ramification_(mathematics) dbr:P-adic_analysis dbr:Dirichlet_L-function dbr:Discrete_valuation_ring dbr:Unique_factorization_domain dbr:Ring_of_integers dbr:Algebraic_curve dbr:Riemann_surface dbr:Unit_(ring_theory) dbr:Homogeneous_function dbr:Rational_number dbr:Prime_element dbr:Totally_real_number_field dbr:Noetherian_ring dbr:Maximal_ideal dbr:Fundamental_theorem_of_Galois_theory dbr:Root_of_unity dbr:Characteristic_polynomial dbr:Cyclotomic_field dbr:Regular_representation dbr:Primitive_element_theorem dbr:Class_number_problem dbr:Hensel's_lemma dbr:Kurt_Hensel dbr:P-adic_number dbr:Finite_field dbr:Ideal_(ring_theory) dbr:Discriminant dbr:Field_(mathematics) dbr:Imaginary_unit dbr:Invariant_(mathematics) dbr:Ordered_pair dbr:Tuple dbr:Algebraic_integer dbr:Field_trace dbr:Class_number_formula dbr:Degree_of_a_field_extension dbc:Algebraic_number_theory dbr:Symmetric_matrix dbr:Algebraic_closure dbr:Field_extension dbr:Subring dbr:Branched_covering dbr:L-function dbr:Modular_arithmetic dbr:Adele_ring dbr:Adjunction_(field_theory) dbr:Galois_cohomology dbr:Genus_field dbr:Absolute_Galois_group dbr:Complex_conjugate dbr:Resultant dbr:Dirichlet's_unit_theorem dbr:Discriminant_of_an_algebraic_number_field dbr:Duality_(mathematics) dbr:Galois_group dbr:Residue_(complex_analysis) dbr:Field_of_fractions dbr:Brauer_group dbr:Field_norm dbr:Monic_polynomial dbr:Scheme_(mathematics) dbr:Local_ring dbr:Global_field dbr:Absolute_value_(algebra) dbr:Algebraic_function_field dbr:Function_field_of_an_algebraic_variety dbr:List_of_number_fields_with_class_number_one dbr:Preimage dbr:S-unit dbr:Primitive_element_(field_theory) dbr:Place_(mathematics) dbr:Discrete_valuation dbr:Vector_addition dbr:Topological_field dbr:Coordinate_ring dbr:Unramified_morphism dbr:Gaussian_rational dbr:Gauss dbr:Springer-Verlag dbr:Regulator_(mathematics) dbr:Splitting_of_prime_ideals_in_Galois_extensions dbr:Dedekind_ring dbr:Localization_of_a_ring dbr:Artin_reciprocity_law dbr:Local-global_principle dbr:Group_action_(mathematics) dbr:Decomposition_group dbr:Frobenius_map dbr:Algebraic_field_extension dbr:Algebraic_numbers dbr:Euler_totient_function dbr:Extension_field dbr:Hamel_dimension dbr:Kummer_extension dbr:Ray_class_group dbr:Real_and_complex_embeddings dbr:Real_part dbr:Idele dbr:Idele_class_group dbr:Completion_(ring_theory) dbr:Coprime dbr:Countable dbr:Riemann_zeta-function dbr:Inertia_group dbr:Integral_basis dbr:Invertible dbr:Poitou-Tate_duality dbr:Roots_of_unity dbr:Null_sequence dbr:Power_basis dbr:Power_integral_basis dbr:Prime_ideal_of_a_valuation dbr:Ultrametric dbr:Uncountable dbr:Matrix_(math) dbr:Matrix_product dbr:Square-free dbr:Zero_divisors dbr:Tamagawa_measure dbr:Tamagawa_number_conjecture dbr:Totally_complex_number_field dbr:Trace_form dbr:File:Schematic_depiction_of_ramification.svg
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Ring_theory_sidebar dbt:Citation dbt:Main dbt:Overline dbt:Short_description
dct:subject	dbc:Field_(mathematics) dbc:Algebraic_number_theory
gold:hypernym	dbr:Extension
rdfs:label	Алгебраическое числовое поле (ru) Algebraic number field (en) Číselné těleso (cs) Cos dels nombres algebraics (ca) Σώμα Αριθμών (el) Algebraischer Zahlkörper (de) حقل الأعداد الجبرية (ar) Cuerpo de números algebraicos (es) Medan bilangan aljabar (in) Corps de nombres (fr) 代数体 (ja) Campo di numeri (it) 대수적 수체 (ko) Ciało liczbowe (pl) Corpo de números algébricos (pt) Algebraïsch getallenlichaam (nl) Алгебраїчне числове поле (uk) Algebraisk talkropp (sv) 代数数域 (zh)
owl:sameAs	freebase:Algebraic number field wikidata:Algebraic number field dbpedia-de:Algebraic number field dbpedia-es:Algebraic number field dbpedia-it:Algebraic number field dbpedia-nl:Algebraic number field dbpedia-pl:Algebraic number field dbpedia-fr:Algebraic number field dbpedia-he:Algebraic number field dbpedia-ja:Algebraic number field dbpedia-pt:Algebraic number field dbpedia-ru:Algebraic number field dbpedia-zh:Algebraic number field dbpedia-sv:Algebraic number field dbpedia-vi:Algebraic number field dbpedia-be:Algebraic number field dbpedia-el:Algebraic number field dbpedia-id:Algebraic number field dbpedia-ko:Algebraic number field dbpedia-ca:Algebraic number field dbpedia-et:Algebraic number field dbpedia-ar:Algebraic number field dbpedia-ast:Algebraic number field dbpedia-ba:Algebraic number field dbpedia-cs:Algebraic number field dbpedia-fa:Algebraic number field dbpedia-fi:Algebraic number field dbpedia-gl:Algebraic number field dbpedia-hi:Algebraic number field dbpedia-nn:Algebraic number field dbpedia-simple:Algebraic number field dbpedia-sl:Algebraic number field dbpedia-sr:Algebraic number field dbpedia-ta:Algebraic number field dbpedia-uk:Algebraic number field dbpedia-global:Algebraic number field
prov:wasDerivedFrom	wikipedia-en:Algebraic_number_field?oldid=1311929519&ns=0
foaf:depiction	wiki-commons:Special:FilePath/Schematic_depiction_of_ramification.svg
foaf:isPrimaryTopicOf	wikipedia-en:Algebraic_number_field
is dbo:wikiPageRedirects of	dbr:Number_field dbr:Dedekind_discriminant_theorem dbr:Degree_of_a_number_field dbr:Degree_of_an_algebraic_number_field dbr:Algebraic_number_fields dbr:Number_fields dbr:Power_basis
is dbo:wikiPageWikiLink of	dbr:Local_field dbr:Ideal_norm dbr:List_of_abstract_algebra_topics dbr:List_of_algebraic_number_theory_topics dbr:List_of_commutative_algebra_topics dbr:Algebraic_number_theory dbr:Hilbert's_twelfth_problem dbr:Kronecker–Weber_theorem dbr:Wieferich_prime dbr:Eisenstein_integer dbr:Birch's_theorem dbr:Quadratic_reciprocity dbr:Cubic_field dbr:Basic_Number_Theory dbr:Pythagorean_field dbr:Noetherian_scheme dbr:Eisenstein_reciprocity dbr:Minimal_polynomial_(field_theory) dbr:Albert–Brauer–Hasse–Noether_theorem dbr:Monogenic_field dbr:4 dbr:John_Tate_(mathematician) dbr:General_number_field_sieve dbr:Dessin_d'enfant dbr:Algebraic_extension dbr:Dedekind_zeta_function dbr:Fractional_ideal dbr:Emmy_Noether dbr:Group_theory dbr:Number_theory dbr:Richard_Dedekind dbr:Maple_(software) dbr:Stark_conjectures dbr:Characteristic_(algebra) dbr:Hilbert's_ninth_problem dbr:Algebraic_K-theory dbr:Cole_Prize dbr:Euclidean_space dbr:Integer dbr:Ludwig_Stickelberger dbr:Prime_number dbr:Algebraic_number dbr:System_of_polynomial_equations dbr:Solving_quadratic_equations_with_continued_fractions dbr:Divisor_(algebraic_geometry) dbr:KANT_(software) dbr:Binary_quadratic_form dbr:Euclidean_domain dbr:Transcendental_function dbr:Ideal_class_group dbr:Artin_transfer_(group_theory) dbr:Serre_group dbr:Golden_ratio dbr:Langlands_program dbr:Chebotarev's_density_theorem dbr:Harmonious_set dbr:Manjul_Bhargava dbr:Riemann_hypothesis dbr:Ramification_(mathematics) dbr:Artin–Verdier_duality dbr:Valuation_(algebra) dbr:Principalization_(algebra) dbr:List_of_inventions_and_discoveries_by_women dbr:Ring_of_integers dbr:Quaternion_algebra dbr:Euclidean_field dbr:Øystein_Ore dbr:Rational_number dbr:Matroid_representation dbr:Uwe_Jannsen dbr:Primitive_element_theorem dbr:Quartic_reciprocity dbr:Brauer–Siegel_theorem dbr:E-function dbr:P-adic_number dbr:Principal_ideal_theorem dbr:Robert_Remak_(mathematician) dbr:Roth's_theorem dbr:Siegel_G-function dbr:Witt_vector dbr:Field_(mathematics) dbr:Field_trace dbr:Analytic_subgroup_theorem dbr:Tate's_algorithm dbr:Tate_duality dbr:Tate_module dbr:Field_extension dbr:Automorphic_form dbr:Hilbert's_tenth_problem dbr:Hasse–Weil_zeta_function dbr:Weil_restriction dbr:Weil–Châtelet_group dbr:List_of_unsolved_problems_in_mathematics dbr:Adele_ring dbr:Degree dbr:Special_number_field_sieve dbr:C._P._Ramanujam dbr:Regular_icosahedron dbr:Genus_field dbr:Stark–Heegner_theorem dbr:Discriminant_of_an_algebraic_number_field dbr:List_of_volunteer_computing_projects dbr:Helmut_Koch dbr:Klein_polyhedron dbr:Equation_xy_=_yx dbr:Field_norm dbr:Quadratic_irrational_number dbr:Gauss's_lemma_(number_theory) dbr:Different_ideal dbr:Modulus_(algebraic_number_theory) dbr:Global_field dbr:Stufe_(algebra) dbr:Abstract_analytic_number_theory dbr:Cyclotomic_unit dbr:Ferrero–Washington_theorem dbr:Krasner's_lemma dbr:Hilbert's_eleventh_problem dbr:Locally_compact_field dbr:Bost–Connes_system dbr:Permutation_polynomial dbr:Thin_set_(Serre) dbr:Parshin_chain dbr:Neukirch–Uchida_theorem dbr:Microbial_enhanced_oil_recovery dbr:Langlands–Shahidi_method dbr:Norm_form dbr:Number_field dbr:Gaussian_rational dbr:List_of_mathematical_symbols_by_subject dbr:Minimal_polynomial_of_2cos(2pi/n) dbr:Hypertranscendental_function dbr:Serre's_property_FA dbr:Shimizu_L-function dbr:Minkowski_space_(number_field) dbr:Conductor_(ring_theory) dbr:Ring_class_field dbr:List_of_things_named_after_Charles_Hermite dbr:Dedekind–Kummer_theorem dbr:Leopoldt's_conjecture dbr:Power_residue_symbol dbr:Bauerian_extension dbr:Dedekind_discriminant_theorem dbr:Degree_of_a_number_field dbr:Degree_of_an_algebraic_number_field dbr:Algebraic_number_fields dbr:Number_fields dbr:Power_basis
is foaf:primaryTopic of	wikipedia-en:Algebraic_number_field