@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-L1L0WF59-4
  skos:prefLabel "corps commutatif"@fr, "field"@en ;
  a skos:Concept ;
  skos:narrower psr:-KTBMST62-P .

psr:-S0STN89F-1
  skos:prefLabel "Diophantine geometry"@en, "géométrie diophantienne"@fr ;
  a skos:Concept ;
  skos:narrower psr:-KTBMST62-P .

psr: a skos:ConceptScheme .
psr:-PJSZQ3B9-1
  skos:prefLabel "Diophantine equation"@en, "équation diophantienne"@fr ;
  a skos:Concept ;
  skos:related psr:-KTBMST62-P .

psr:-KTBMST62-P
  skos:definition """En mathématiques, un corps <i>K</i> est dit <b>quasi-algébriquement clos</b> si tout polynôme homogène <i>P</i> sur <i>K</i> 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 <i>P</i> à coefficients dans <i>K</i>, homogène, non constant, en les variables <i>X</i><sub>1</sub>, …, <i>X<sub>N</sub></i> et de degré <i>d &lt; N</i>, il existe un zéro non trivial de <i>P</i> sur <i>K</i>, c'est-à-dire des éléments <i>x</i><sub>1</sub>, …, <i>x<sub>N</sub></i> de <i>K</i> non tous nuls tels que <i>P</i>(<i>x</i><sub>1</sub>, …, <i>x<sub>N</sub></i>) = 0.  
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Corps_quasi-alg%C3%A9briquement_clos">https://fr.wikipedia.org/wiki/Corps_quasi-alg%C3%A9briquement_clos</a>)"""@fr, """In mathematics, a field <i>F</i> is called <b>quasi-algebraically closed</b> (or <b><i>C</i><sub>1</sub></b>) if every non-constant homogeneous polynomial <i>P</i> over <i>F</i> 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 (Tsen 1936); and later by Serge Lang in his 1951 Princeton University dissertation and in his 1952 paper (Lang 1952). The idea itself is attributed to Lang's advisor Emil Artin. Formally, if <i>P</i> is a non-constant homogeneous polynomial in variables  <dl><dd><i>X</i><sub>1</sub>, ..., <i>X</i><sub><i>N</i></sub>,</dd></dl> and of degree <i>d</i> satisfying  <dl><dd><i>d</i> &lt; <i>N</i></dd></dl> then it has a non-trivial zero over <i>F</i>; that is, for some <i>x</i><sub><i>i</i></sub> in <i>F</i>, not all 0, we have  <dl><dd><i>P</i>(<i>x</i><sub>1</sub>, ..., <i>x</i><sub><i>N</i></sub>) = 0.</dd></dl> In geometric language, the hypersurface defined by <i>P</i>, in projective space of degree <span class="nowrap"><i>N</i> − 2</span>,  then has a point over <i>F</i>.  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Quasi-algebraically_closed_field">https://en.wikipedia.org/wiki/Quasi-algebraically_closed_field</a>)"""@en ;
  skos:broader psr:-L1L0WF59-4, psr:-S0STN89F-1 ;
  skos:prefLabel "corps quasi-algébriquement clos"@fr, "quasi-algebraically closed field"@en ;
  skos:inScheme psr: ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Corps_quasi-alg%C3%A9briquement_clos>, <https://en.wikipedia.org/wiki/Quasi-algebraically_closed_field> ;
  skos:related psr:-PJSZQ3B9-1 ;
  a skos:Concept ;
  dc:created "2023-08-24"^^xsd:date ;
  dc:modified "2024-10-18"^^xsd:date .