About: Ordered field

Property	Value
dbo:description	camp juntament amb una ordenació total dels seus elements de manera que el conjunt d'elements positius sigui invariant de translació i tancat multiplicativament (ca) алгебрична структура, що складається з тіла та відповідного розташування його елементів (uk) ciało z porządkiem zupełnym na jego elementach, który jest zgodny z działaniami w ciele (pl) Algebraische Struktur (de) algebraická struktura skládající se z tělesa a příslušného uspořádání jeho prvků (cs) bidang bersama dengan urutan total elemennya yang kompatibel dengan operasi bidang (in) komuta korpo kune kun totala ordo sur ĝiaj elementoj tia, ke la subaro de pozitivaj elementoj estas multiplike fermita kaj translacie invarianta (eo) field together with a total ordering of its elements such that the set of positive elements is translation-invariant and multiplicatively closed (en) 체 연산과 호환되는 전순서를 갖춘 체 (ko)
dbo:thumbnail	wiki-commons:Special:FilePath/Invariance_of_less-th...on_with_positive_number.svg?width=300
dbo:wikiPageExternalLink	https://archive.org/details/orderingsvaluati0000lamt
dbo:wikiPageWikiLink	dbr:Archimedean_property dbc:Ordered_groups dbr:Axiomatization dbr:Superreal_number dbr:Non-Archimedean_ordered_field dbr:Formally_real_field dbr:Otto_Hölder dbr:Class_(set_theory) dbr:Product_topology dbr:Real_closed_field dbc:Real_algebraic_geometry dbr:Complex_number dbr:Imaginary_unit dbr:Real_number dbr:Inner_product_space dbr:Set_(mathematics) dbr:Vector_space dbr:Examples_of_vector_spaces dbr:Hans_Hahn_(mathematician) dbr:Square_(algebra) dbr:Hensel's_lemma dbr:Mathematics dbr:Infinitesimal dbr:Computable_number dbr:Order_topology dbr:Characteristic_(algebra) dbr:Isomorphism dbr:Discrete_topology dbr:Subset dbr:Rational_number dbr:David_Hilbert dbr:Field_extension dbr:Field_(mathematics) dbr:Topological_field dbr:Boolean_space dbr:Polynomial dbr:American_Mathematical_Society dbr:Subgroup dbr:Subspace_topology dbc:Ordered_algebraic_structures dbr:Transitive_property dbr:Finite_field dbr:Continuous_function_(topology) dbr:Convex_analysis dbr:Compact_space dbr:Formal_power_series dbr:Natural_number dbr:Zorn's_lemma dbr:Hausdorff_space dbr:Total_order dbr:Totally_disconnected_space dbr:Hyperreal_number dbr:Graduate_Studies_in_Mathematics dbr:Real_coordinate_space dbr:Orientation_(vector_space) dbr:Transseries dbr:Subbasis dbr:Archimedean_field dbr:Least_upper_bound dbr:Binary_predicate dbr:Dedekind-complete dbr:P-adic_numbers dbr:Hyperreal_numbers dbr:Rational_functions dbr:Real_numbers dbr:Algebraic_numbers dbr:Artin–Schreier_theorem dbr:Surreal_numbers dbr:File:Invariance_of_less-than-relation_by_multiplication_with_positive_number.svg dbr:File:Translation_invariance_of_less-than-relation.svg
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Reflist dbt:Anchor dbt:Radic dbt:Num dbt:Citation dbt:Visible_anchor dbt:Em dbt:Lang_Algebra dbt:Annotated_link dbt:Short_description dbt:Order_theory
dct:subject	dbc:Ordered_groups dbc:Real_algebraic_geometry dbc:Ordered_algebraic_structures
gold:hypernym	dbr:Field
rdfs:label	Ordered field (en) حقل مرتب (ar) Geordneter Körper (de) Cuerpo ordenado (es) Corps ordonné (fr) Medan terurut (in) 順序体 (ja) Campo ordinato (it) 순서체 (ko) Ciało uporządkowane (pl) Corpo ordenado (pt) Упорядоченное поле (ru) Впорядковане поле (uk) 有序域 (zh)
owl:sameAs	freebase:Ordered field yago-res:Ordered field wikidata:Ordered field dbpedia-it:Ordered field dbpedia-de:Ordered field dbpedia-fr:Ordered field dbpedia-zh:Ordered field dbpedia-ja:Ordered field dbpedia-pt:Ordered field dbpedia-he:Ordered field dbpedia-da:Ordered field dbpedia-es:Ordered field dbpedia-hu:Ordered field dbpedia-fa:Ordered field dbpedia-ru:Ordered field dbpedia-pl:Ordered field dbpedia-ko:Ordered field dbpedia-id:Ordered field dbpedia-ar:Ordered field dbpedia-sk:Ordered field dbpedia-uk:Ordered field dbpedia-global:Ordered field dbr:Ordered field
prov:wasDerivedFrom	wikipedia-en:Ordered_field?oldid=1279366473&ns=0
foaf:depiction	wiki-commons:Special:FilePath/Invariance_of_less-th...ltiplication_with_positive_number.svg wiki-commons:Special:FilePath/Translation_invariance_of_less-than-relation.svg
foaf:isPrimaryTopicOf	wikipedia-en:Ordered_field
is dbo:wikiPageRedirects of	dbr:Preordered_field dbr:Fan_(order) dbr:Field_ordering dbr:Harrison_set dbr:Harrison_topology dbr:Superordered_field
is dbo:wikiPageWikiLink of	dbr:Archimedean_property dbr:Non-Archimedean_ordered_field dbr:Formally_real_field dbr:Transfer_principle dbr:Real_closed_field dbr:Euclidean_field dbr:Standard_part_function dbr:Complex_number dbr:Number dbr:Real_analysis dbr:Real_number dbr:First-order_logic dbr:Metric_space dbr:Square_(algebra) dbr:Convex_cone dbr:Surreal_number dbr:Pythagorean_field dbr:Hahn_series dbr:Valuation_ring dbr:Puiseux_series dbr:Wilkie's_theorem dbr:4 dbr:P-adic_number dbr:Convex_set dbr:Infinitesimal dbr:Rolle's_theorem dbr:Cayley–Dickson_construction dbr:Existentially_closed_model dbr:Exponential_field dbr:Ordered_exponential_field dbr:Completeness_of_the_real_numbers dbr:Characteristic_(algebra) dbr:Pfaffian_function dbr:Order_(mathematics) dbr:Inequality_(mathematics) dbr:Linear_inequality dbr:Casus_irreducibilis dbr:Global_optimization dbr:Structure_(mathematical_logic) dbr:Rational_number dbr:Oriented_matroid dbr:Line_(geometry) dbr:Operator_(mathematics) dbr:Field_(mathematics) dbr:Algebraic_structure dbr:Discrete_geometry dbr:Ultraproduct dbr:Reverse_mathematics dbr:Gaussian_rational dbr:Mathematical_structure dbr:Nested_intervals dbr:List_of_order_theory_topics dbr:Algebraic_geometry dbr:Nonstandard_analysis dbr:Homogeneous_function dbr:Hilbert's_seventeenth_problem dbr:Locally_convex_topological_vector_space dbr:Construction_of_the_real_numbers dbr:Substructure_(mathematics) dbr:Linear_combination dbr:Total_order dbr:Second-order_logic dbr:Type_(model_theory) dbr:Tarski's_axiomatization_of_the_reals dbr:Definite_quadratic_form dbr:Symmetric_bilinear_form dbr:Glossary_of_field_theory dbr:Ordered_ring dbr:Sylvester–Gallai_configuration dbr:Atomic_model_(mathematical_logic) dbr:Constructive_set_theory dbr:Hyperreal_number dbr:Real_algebraic_geometry dbr:Real_closed_ring dbr:Geometric_Algebra_(book) dbr:Generalised_metric dbr:Model_complete_theory dbr:Preordered_field dbr:Outline_of_algebraic_structures dbr:Real_coordinate_space dbr:Equivalent_definitions_of_mathematical_structures dbr:Fan_(order) dbr:Field_ordering dbr:Harrison_set dbr:Harrison_topology dbr:Superordered_field
is foaf:primaryTopic of	wikipedia-en:Ordered_field