@prefix p: <http://www.wikidata.org/prop/> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix schema1: <http://schema.org/> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix wd: <http://www.wikidata.org/entity/> .
@prefix wds: <http://www.wikidata.org/entity/statement/> .
@prefix wdt: <http://www.wikidata.org/prop/direct/> .
@prefix wdtn: <http://www.wikidata.org/prop/direct-normalized/> .
@prefix wikibase: <http://wikiba.se/ontology#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

wd:Q6433699 rdfs:label "complex de Koszul"@ca,
        "Koszul-Komplex"@de,
        "Koszul complex"@en,
        "komplekso de Koszul"@eo,
        "complexe de Koszul"@fr,
        "コシュル複体"@ja,
        "코쥘 복합체"@ko,
        "ကိုးဇူးလ် ကွန်ပလက်စ်"@my,
        "complexo de Koszul"@pt,
        "complexo de Koszul"@pt-br,
        "комплекс Кошуля"@ru,
        "Koszul kompleksi"@tr,
        "Koszul序列"@yue,
        "Koszul复形"@zh,
        "Koszul复形"@zh-cn,
        "科斯居尔复形"@zh-hans,
        "科斯居爾復形"@zh-hant ;
    schema1:dateModified "2026-09-06T13:45:00+00:00"^^xsd:dateTime ;
    schema1:description "construcció d'àlgebra homològica"@ca,
        "construction of homological algebra used in commutative agebra"@en,
        "конструкция гомологической алгебры, используемая в коммутативной алгебре"@ru ;
    schema1:version 2541102699 ;
    wikibase:identifiers 4 ;
    wikibase:sitelinks 5 ;
    wikibase:statements 13 ;
    skos:altLabel "Koszul複体"@ja,
        "コジュル複体"@ja,
        "コズュル複体"@ja,
        "Koszul complex"@yue,
        "科斯居尔复形"@zh,
        "科斯居尔复形"@zh-cn,
        "Koszul复形"@zh-hans,
        "Koszul復形"@zh-hant ;
    p:P138 wds:Q6433699-6fbc04bf-41b0-340d-6218-5234b1ae721e ;
    p:P2534 wds:Q6433699-9df0501e-4993-0782-d61c-2d6f9d24cd52 ;
    p:P279 wds:Q6433699-38517ae7-4cd4-31cd-4bef-95aa87ba2921 ;
    p:P31 wds:Q6433699-c78784ad-44f1-2670-8f4d-4dda763853bc ;
    p:P4215 wds:Q6433699-65827B90-0655-4F0B-A382-A1E8F370A918 ;
    p:P5555 wds:Q6433699-02215d21-476c-6fc0-5534-5a9f7929f61e ;
    p:P6104 wds:Q6433699-7F0E562E-994B-4D43-B023-333DB6D59628 ;
    p:P6366 wds:Q6433699-5636B490-FE06-4F18-9E90-CD911899F49B ;
    p:P646 wds:Q6433699-41CEE16A-ECB7-49FF-BDA6-B4E43DEDD1CB ;
    p:P7235 wds:Q6433699-9628656a-4cd8-ec51-e3ed-33c768f21495,
        wds:Q6433699-d11ac351-4ab1-6cd1-e8ce-d51a15309504,
        wds:Q6433699-d9aa3569-430f-91b1-34fa-b4f2dee56d22 ;
    p:P7554 wds:Q6433699-fd0dbaca-460d-208e-7844-e44ed4fcd35b ;
    wdtn:P6366 <https://makg.org/entity/2778246876> ;
    wdt:P138 wd:Q526290 ;
    wdt:P2534 "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" displaystyle=\"true\" rowspacing=\"3pt\"><mtr><mtd></mtd><mtd><mi>s</mi><mo stretchy=\"false\">&#x2208;</mo><msup><mi>E</mi><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">&#x2228;</mo></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mn>0</mn><mo stretchy=\"false\" accent=\"false\">&#x2192;</mo><msup><mo stretchy=\"false\">&#x22C0;</mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msub><mi>dim</mi><mrow data-mjx-texclass=\"ORD\"><mi>R</mi></mrow></msub><mi>E</mi></mrow></mrow></msup><mi>E</mi><mrow data-mjx-texclass=\"ORD\"><mover><mrow><mo stretchy=\"false\" accent=\"false\">&#x2192;</mo></mrow><mi>d</mi></mover></mrow><msup><mo stretchy=\"false\">&#x22C0;</mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msub><mi>dim</mi><mrow data-mjx-texclass=\"ORD\"><mi>R</mi></mrow></msub><mi>E</mi><mo stretchy=\"false\">&#x2212;</mo><mn>1</mn></mrow></mrow></msup><mi>E</mi><mo stretchy=\"false\" accent=\"false\">&#x2192;</mo><mo stretchy=\"false\">&#x22EF;</mo><mo stretchy=\"false\" accent=\"false\">&#x2192;</mo><msup><mo stretchy=\"false\">&#x22C0;</mo><mrow data-mjx-texclass=\"ORD\"><mn>1</mn></mrow></msup><mi>E</mi><mrow data-mjx-texclass=\"ORD\"><mover><mrow><mo stretchy=\"false\" accent=\"false\">&#x2192;</mo></mrow><mi>d</mi></mover></mrow><mi>R</mi><mo stretchy=\"false\" accent=\"false\">&#x2192;</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><msub><mi>d</mi><mrow data-mjx-texclass=\"ORD\"><mi>k</mi></mrow></msub><mo stretchy=\"false\">(</mo><msub><mi>e</mi><mrow data-mjx-texclass=\"ORD\"><mn>1</mn></mrow></msub><mo stretchy=\"false\">&#x2227;</mo><mo stretchy=\"false\">&#x22EF;</mo><mo stretchy=\"false\">&#x2227;</mo><msub><mi>e</mi><mrow data-mjx-texclass=\"ORD\"><mi>k</mi></mrow></msub><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">=</mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">&#x2211;</mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i</mi><mo stretchy=\"false\">=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass=\"ORD\"><mi>k</mi></mrow></munderover></mstyle><mo stretchy=\"false\">(</mo><mo stretchy=\"false\">&#x2212;</mo><mn>1</mn><msup><mo stretchy=\"false\">)</mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i</mi><mo stretchy=\"false\">+</mo><mn>1</mn></mrow></mrow></msup><mi>s</mi><mo stretchy=\"false\">(</mo><msub><mi>e</mi><mrow data-mjx-texclass=\"ORD\"><mi>i</mi></mrow></msub><mo stretchy=\"false\">)</mo><msub><mi>e</mi><mrow data-mjx-texclass=\"ORD\"><mn>1</mn></mrow></msub><mo stretchy=\"false\">&#x2227;</mo><mo stretchy=\"false\">&#x22EF;</mo><mo stretchy=\"false\">&#x2227;</mo><msub><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>e</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass=\"ORD\"><mi>i</mi></mrow></msub><mo stretchy=\"false\">&#x2227;</mo><mo stretchy=\"false\">&#x22EF;</mo><mo stretchy=\"false\">&#x2227;</mo><msub><mi>e</mi><mrow data-mjx-texclass=\"ORD\"><mi>k</mi></mrow></msub></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML> ;
    wdt:P279 wd:Q125379340 ;
    wdt:P31 wd:Q24034552 ;
    wdt:P4215 "Koszul complex" ;
    wdt:P5555 <http://commons.wikimedia.org/wiki/Special:FilePath/Koszul2.png> ;
    wdt:P6104 wd:Q8487137 ;
    wdt:P6366 "2778246876" ;
    wdt:P646 "/m/02kz0y" ;
    wdt:P7235 "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mi>E</mi></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mi>R</mi></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML>,
        "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><msup><mi>E</mi><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">&#x2228;</mo></mrow></msup></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML> ;
    wdt:P7554 "Koszul_complex" .