Browse Wiki & Semantic Web
| Http://dbpedia.org/resource/Quasi-algebraically closed field |
| This page has no properties. |
| hide properties that link here |
| No properties link to this page. |
| http://dbpedia.org/resource/Quasi-algebraically_closed_field |
| http://dbpedia.org/ontology/abstract | In mathematics, a field F is called quasi- … In mathematics, a field F is called quasi-algebraically closed (or C1) if every non-constant homogeneous polynomial P over F has a non-trivial zero provided the number of its variables is more than its degree. The idea of quasi-algebraically closed fields was investigated by C. C. Tsen, a student of Emmy Noether, in a 1936 paper; and later by Serge Lang in his 1951 Princeton University dissertation and in his 1952 paper. The idea itself is attributed to Lang's advisor Emil Artin. Formally, if P is a non-constant homogeneous polynomial in variables X1, ..., XN, and of degree d satisfying d < N then it has a non-trivial zero over F; that is, for some xi in F, not all 0, we have P(x1, ..., xN) = 0. In geometric language, the hypersurface defined by P, in projective space of degree N − 2, then has a point over F. of degree N − 2, then has a point over F. , En mathématiques, un corps K est dit quasi … En mathématiques, un corps K est dit quasi-algébriquement clos si tout polynôme homogène P sur K non constant possède un zéro non trivial dès que le nombre de ses variables est strictement supérieur à son degré, autrement dit : si pour tout polynôme P à coefficients dans K, homogène, non constant, en les variables X1, …, XN et de degré d < N, il existe un zéro non trivial de P sur K, c'est-à-dire des éléments x1, …, xN de K non tous nuls tels que P(x1, …, xN) = 0. En termes géométriques, l'hypersurface définie par P, dans l'espace projectif de dimension N – 1, possède alors un point sur K. Cette notion a été d'abord étudiée par Chiungtze Tsen, un étudiant d'Emmy Noether, dans un article de 1936, puis par Serge Lang en 1951 dans sa thèse. L'idée elle-même est attribuée à Emil Artin.idée elle-même est attribuée à Emil Artin. |
|---|---|
| http://dbpedia.org/ontology/wikiPageID | 2934213 |
| http://dbpedia.org/ontology/wikiPageLength | 9646 |
| http://dbpedia.org/ontology/wikiPageRevisionID | 988469482 |
| http://dbpedia.org/ontology/wikiPageWikiLink | http://dbpedia.org/resource/Field_%28mathematics%29 + , http://dbpedia.org/resource/Algebraic_function_field + , http://dbpedia.org/resource/Cambridge_University_Press + , http://dbpedia.org/resource/Ax%E2%80%93Kochen_theorem + , http://dbpedia.org/resource/Chevalley%E2%80%93Warning_theorem + , http://dbpedia.org/resource/Pseudo_algebraically_closed_field + , http://dbpedia.org/resource/Diophantine_dimension + , http://dbpedia.org/resource/Guy_Terjanian + , http://dbpedia.org/resource/Finite_field + , http://dbpedia.org/resource/Primary_extension + , http://dbpedia.org/resource/Springer-Verlag + , http://dbpedia.org/resource/P-adic_field + , http://dbpedia.org/resource/Homogeneous_polynomial + , http://dbpedia.org/resource/Tsen%27s_theorem + , http://dbpedia.org/resource/Tsen_rank + , http://dbpedia.org/resource/Category:Field_%28mathematics%29 + , http://dbpedia.org/resource/Reduced_norm + , http://dbpedia.org/resource/Princeton_University + , http://dbpedia.org/resource/Graduate_Texts_in_Mathematics + , http://dbpedia.org/resource/Serge_Lang + , http://dbpedia.org/resource/Subvariety + , http://dbpedia.org/resource/Brauer%27s_theorem_on_forms + , http://dbpedia.org/resource/Algebraically_closed_field + , http://dbpedia.org/resource/Mathematics + , http://dbpedia.org/resource/Brauer_group + , http://dbpedia.org/resource/Annals_of_Mathematics + , http://dbpedia.org/resource/Zariski_topology + , http://dbpedia.org/resource/Local_Fields + , http://dbpedia.org/resource/Characteristic_%28algebra%29 + , http://dbpedia.org/resource/Projective_space + , http://dbpedia.org/resource/Model_theory + , http://dbpedia.org/resource/Transcendence_degree + , http://dbpedia.org/resource/Isotropic_quadratic_form + , http://dbpedia.org/resource/Emil_Artin + , http://dbpedia.org/resource/Category:Diophantine_geometry + , http://dbpedia.org/resource/Cohomological_dimension_of_a_field + , http://dbpedia.org/resource/C._C._Tsen + , http://dbpedia.org/resource/Emmy_Noether + , http://dbpedia.org/resource/Hypersurface + , http://dbpedia.org/resource/Perfect_field + |
| http://dbpedia.org/property/wikiPageUsesTemplate | http://dbpedia.org/resource/Template:Reflist + , http://dbpedia.org/resource/Template:Citation + , http://dbpedia.org/resource/Template:Cite_journal + , http://dbpedia.org/resource/Template:Cite_book + , http://dbpedia.org/resource/Template:Harv + |
| http://purl.org/dc/terms/subject | http://dbpedia.org/resource/Category:Field_%28mathematics%29 + , http://dbpedia.org/resource/Category:Diophantine_geometry + |
| http://www.w3.org/ns/prov#wasDerivedFrom | http://en.wikipedia.org/wiki/Quasi-algebraically_closed_field?oldid=988469482&ns=0 + |
| http://xmlns.com/foaf/0.1/isPrimaryTopicOf | http://en.wikipedia.org/wiki/Quasi-algebraically_closed_field + |
| owl:sameAs | http://rdf.freebase.com/ns/m.08dnfp + , http://dbpedia.org/resource/Quasi-algebraically_closed_field + , https://global.dbpedia.org/id/2e1X3 + , http://yago-knowledge.org/resource/Quasi-algebraically_closed_field + , http://fr.dbpedia.org/resource/Corps_quasi-alg%C3%A9briquement_clos + , http://www.wikidata.org/entity/Q283684 + |
| rdf:type | http://dbpedia.org/class/yago/Statement106722453 + , http://dbpedia.org/class/yago/WikicatDiophantineEquations + , http://dbpedia.org/class/yago/Message106598915 + , http://dbpedia.org/class/yago/Communication100033020 + , http://dbpedia.org/class/yago/Abstraction100002137 + , http://dbpedia.org/class/yago/MathematicalStatement106732169 + , http://dbpedia.org/class/yago/Equation106669864 + |
| rdfs:comment | En mathématiques, un corps K est dit quasi … En mathématiques, un corps K est dit quasi-algébriquement clos si tout polynôme homogène P sur K non constant possède un zéro non trivial dès que le nombre de ses variables est strictement supérieur à son degré, autrement dit : si pour tout polynôme P à coefficients dans K, homogène, non constant, en les variables X1, …, XN et de degré d < N, il existe un zéro non trivial de P sur K, c'est-à-dire des éléments x1, …, xN de K non tous nuls tels que P(x1, …, xN) = 0. En termes géométriques, l'hypersurface définie par P, dans l'espace projectif de dimension N – 1, possède alors un point sur K.nsion N – 1, possède alors un point sur K. , In mathematics, a field F is called quasi- … In mathematics, a field F is called quasi-algebraically closed (or C1) if every non-constant homogeneous polynomial P over F has a non-trivial zero provided the number of its variables is more than its degree. The idea of quasi-algebraically closed fields was investigated by C. C. Tsen, a student of Emmy Noether, in a 1936 paper; and later by Serge Lang in his 1951 Princeton University dissertation and in his 1952 paper. The idea itself is attributed to Lang's advisor Emil Artin. Formally, if P is a non-constant homogeneous polynomial in variables X1, ..., XN, and of degree d satisfyinges X1, ..., XN, and of degree d satisfying |
| rdfs:label | Quasi-algebraically closed field , Corps quasi-algébriquement clos |
| hide properties that link here |
