@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:-RHXBWN0G-4
  skos:prefLabel "anneau"@fr, "ring"@en ;
  a skos:Concept ;
  skos:narrower psr:-R2X1SGRQ-V .

psr:-G09XWL0P-S
  skos:prefLabel "anneau canonique"@fr, "canonical ring"@en ;
  a skos:Concept ;
  skos:broader psr:-R2X1SGRQ-V .

psr:-WK4R6NV8-P
  skos:prefLabel "idéal différentiel"@fr, "differential ideal"@en ;
  a skos:Concept ;
  skos:broader psr:-R2X1SGRQ-V .

psr: a skos:ConceptScheme .
psr:-R2X1SGRQ-V
  a skos:Concept ;
  skos:prefLabel "algèbre graduée"@fr, "graded ring"@en ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Graded_ring>, <https://fr.wikipedia.org/wiki/Alg%C3%A8bre_gradu%C3%A9e> ;
  skos:narrower psr:-G09XWL0P-S, psr:-WK4R6NV8-P ;
  dc:modified "2023-08-23"^^xsd:date ;
  skos:broader psr:-RHXBWN0G-4 ;
  skos:inScheme psr: ;
  skos:definition """In mathematics, in particular abstract algebra, a graded ring is a ring such that the underlying additive group is a direct sum of abelian groups <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 R_{i}}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <msub>
         <mi>R</mi>
         <mrow class="MJX-TeXAtom-ORD">
         <mi>i</mi>
         </mrow>
         </msub>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle R_{i}}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db421291be9d0103404ced7495b363437b67b6b1" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.564ex; height:2.509ex;" alt="R_{i}"></span> such that <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 R_{i}R_{j}\\\\subseteq R_{i+j}}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <msub>
         <mi>R</mi>
         <mrow class="MJX-TeXAtom-ORD">
         <mi>i</mi>
         </mrow>
         </msub>
         <msub>
         <mi>R</mi>
         <mrow class="MJX-TeXAtom-ORD">
         <mi>j</mi>
         </mrow>
         </msub>
         <mo>⊆<!-- ⊆ --></mo>
         <msub>
         <mi>R</mi>
         <mrow class="MJX-TeXAtom-ORD">
         <mi>i</mi>
         <mo>+</mo>
         <mi>j</mi>
         </mrow>
         </msub>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle R_{i}R_{j}\\\\subseteq R_{i+j}}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ab8739142b5cbef1b8c17287d5cbdf34f00c15b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.856ex; height:2.843ex;" alt="R_{i}R_{j}\\\\subseteq R_{{i+j}}"></span>. The index set is usually the set of nonnegative integers or the set of integers, but can be any monoid. The direct sum decomposition is usually referred to as gradation or grading. A graded module is defined similarly. It generalizes graded vector spaces. A graded module that is also a graded ring is called a graded algebra. A graded ring could also be viewed as a graded Z-algebra. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Graded_ring">https://en.wikipedia.org/wiki/Graded_ring</a>)"""@en, """En mathématiques, en algèbre linéaire, on appelle algèbre graduée une algèbre dotée d'une structure supplémentaire, appelée graduation. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Alg%C3%A8bre_gradu%C3%A9e">https://fr.wikipedia.org/wiki/Alg%C3%A8bre_gradu%C3%A9e</a>)"""@fr ;
  dc:created "2023-08-23"^^xsd:date .