@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:-LLND57KL-D
  skos:prefLabel "algèbre associative"@fr, "associative algebra"@en ;
  a skos:Concept ;
  skos:narrower psr:-N2M3QNK0-Q .

psr:-VL4MDL0Q-G
  skos:prefLabel "opération binaire"@fr, "binary operation"@en ;
  a skos:Concept ;
  skos:narrower psr:-N2M3QNK0-Q .

psr:-N2M3QNK0-Q
  dc:created "2023-08-24"^^xsd:date ;
  dc:modified "2023-08-24"^^xsd:date ;
  a skos:Concept ;
  skos:broader psr:-LLND57KL-D, psr:-VL4MDL0Q-G, psr:-F1B5QL5S-0 ;
  skos:prefLabel "algèbre flexible"@fr, "flexible algebra"@en ;
  skos:inScheme psr: ;
  skos:definition """In mathematics, particularly abstract algebra, a binary operation • on a set is <b>flexible</b> if it satisfies the <b>flexible identity</b>:
         
         <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle a\\ullet \\\\left(b\\ullet a\\
ight)=\\\\left(a\\ullet b\\
ight)\\ullet a}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>a</mi>
         <mo>∙<!-- ∙ --></mo>
         <mrow>
         <mo>(</mo>
         <mrow>
         <mi>b</mi>
         <mo>∙<!-- ∙ --></mo>
         <mi>a</mi>
         </mrow>
         <mo>)</mo>
         </mrow>
         <mo>=</mo>
         <mrow>
         <mo>(</mo>
         <mrow>
         <mi>a</mi>
         <mo>∙<!-- ∙ --></mo>
         <mi>b</mi>
         </mrow>
         <mo>)</mo>
         </mrow>
         <mo>∙<!-- ∙ --></mo>
         <mi>a</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle a\\ullet \\\\left(b\\ullet a\\
ight)=\\\\left(a\\ullet b\\
ight)\\ullet a}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6938927f38c5381e510a43f5239c5fed22c1998f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.41ex; height:2.843ex;" alt="{\\\\displaystyle a\\ullet \\\\left(b\\ullet a\\
ight)=\\\\left(a\\ullet b\\
ight)\\ullet a}"></span></dd></dl>
         for any two elements <i>a</i> and <i>b</i> of the set. A magma (that is, a set equipped with a binary operation) is flexible if the binary operation with which it is equipped is flexible. Similarly, a nonassociative algebra is flexible if its multiplication operator is flexible.
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Flexible_algebra">https://en.wikipedia.org/wiki/Flexible_algebra</a>)"""@en, """En mathématiques, en particulier en algèbre, une opération binaire • sur un ensemble est dite flexible si l'identité flexible est satisfaite :  <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\\\\displaystyle a\\ullet \\\\left(b\\ullet a\\
ight)=\\\\left(a\\ullet b\\
ight)\\ullet a}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>a</mi>
         <mo>∙<!-- ∙ --></mo>
         <mrow>
         <mo>(</mo>
         <mrow>
         <mi>b</mi>
         <mo>∙<!-- ∙ --></mo>
         <mi>a</mi>
         </mrow>
         <mo>)</mo>
         </mrow>
         <mo>=</mo>
         <mrow>
         <mo>(</mo>
         <mrow>
         <mi>a</mi>
         <mo>∙<!-- ∙ --></mo>
         <mi>b</mi>
         </mrow>
         <mo>)</mo>
         </mrow>
         <mo>∙<!-- ∙ --></mo>
         <mi>a</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle a\\ullet \\\\left(b\\ullet a\\
ight)=\\\\left(a\\ullet b\\
ight)\\ullet a}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6938927f38c5381e510a43f5239c5fed22c1998f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.41ex; height:2.843ex;" alt="{\\\\displaystyle a\\ullet \\\\left(b\\ullet a\\
ight)=\\\\left(a\\ullet b\\
ight)\\ullet a}"></span></dd></dl>
         pour tous <i>a</i> et <i>b</i> dans l'ensemble. Un magma (c'est-à-dire un ensemble muni d'une opération binaire) est flexible si l'opération binaire dont il est muni est flexible. De même, une algèbre non associative est flexible si son produit est flexible. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Alg%C3%A8bre_flexible">https://fr.wikipedia.org/wiki/Alg%C3%A8bre_flexible</a>)"""@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Alg%C3%A8bre_flexible>, <https://en.wikipedia.org/wiki/Flexible_algebra> .

psr:-F1B5QL5S-0
  skos:prefLabel "algèbre non associative"@fr, "non-associative algebra"@en ;
  a skos:Concept ;
  skos:narrower psr:-N2M3QNK0-Q .

psr: a skos:ConceptScheme .