@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: a skos:ConceptScheme .
psr:-F1B5QL5S-0
  skos:prefLabel "algèbre non associative"@fr, "non-associative algebra"@en ;
  a skos:Concept ;
  skos:narrower psr:-GD2PCT10-B .

psr:-GD2PCT10-B
  dc:created "2023-08-24"^^xsd:date ;
  skos:broader psr:-X4R4FW27-X, psr:-F1B5QL5S-0 ;
  skos:definition """In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the real numbers, usually represented by the capital letter S, boldface <span class="texhtml"><b>S</b></span> or blackboard bold <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 \\\\mathbb {S} }">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="double-struck">S</mi>
         </mrow>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {S} }</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f9d5874c5d7f68eba1cec9da9ccbe53903303bb" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.293ex; height:2.176ex;" alt="{\\\\mathbb  S}"></span>. They are obtained by applying the Cayley–Dickson construction to the octonions, and as such the octonions are isomorphic to a subalgebra of the sedenions. Unlike the octonions, the sedenions are not an alternative algebra. Applying the Cayley–Dickson construction to the sedenions yields a 32-dimensional algebra, sometimes called the 32-ions or trigintaduonions. It is possible to continue applying the Cayley–Dickson construction arbitrarily many times. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Sedenion">https://en.wikipedia.org/wiki/Sedenion</a>)"""@en, """En mathématiques, les sédénions forment une algèbre réelle de dimension 16, notée <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 \\\\mathbb {S} }">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="double-struck">S</mi>
         </mrow>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {S} }</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f9d5874c5d7f68eba1cec9da9ccbe53903303bb" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.293ex; height:2.176ex;" alt="{\\\\mathbb  S}"></span>. Leur nom provient du latin sedecim qui veut dire seize. Deux sortes sont actuellement connues :
<br/>- les sédénions obtenus par application de la construction de Cayley-Dickson;
<br/>- les sédénions coniques (ou algèbre M). 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/S%C3%A9d%C3%A9nion">https://fr.wikipedia.org/wiki/S%C3%A9d%C3%A9nion</a>)"""@fr ;
  skos:inScheme psr: ;
  skos:prefLabel "sedenion"@en, "sédénion"@fr ;
  a skos:Concept ;
  dc:modified "2023-08-24"^^xsd:date ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Sedenion>, <https://fr.wikipedia.org/wiki/S%C3%A9d%C3%A9nion> .

psr:-X4R4FW27-X
  skos:prefLabel "hypercomplex number"@en, "nombre hypercomplexe"@fr ;
  a skos:Concept ;
  skos:narrower psr:-GD2PCT10-B .