Koszul complex
construction of homological algebra used in commutative agebra
| rdfs:label |
"Koszul complex"@en
|
|
skos:alt |
"Koszul複体"@ja
"コジュル複体"@ja
"コズュル複体"@ja
|
| schema:description |
"construction of homological algebra used in commutative agebra"@en
|
|
schema:date |
"2026-09-06T13:45:00+00:00"^^xsd:dateTime |
| schema:version | 2541102699 |
| wikibase:identifiers | 4 |
| wikibase:sitelinks | 5 |
| wikibase:statements | 13 |
| p:P138 | wd:statement/Q6433699-6fbc04bf-41b0-340d-6218-5234b1ae721e |
| p:P2534 | wd:statement/Q6433699-9df0501e-4993-0782-d61c-2d6f9d24cd52 |
| p:P279 | wd:statement/Q6433699-38517ae7-4cd4-31cd-4bef-95aa87ba2921 |
| p:P31 | wd:statement/Q6433699-c78784ad-44f1-2670-8f4d-4dda763853bc |
| p:P4215 | wd:statement/Q6433699-65827B90-0655-4F0B-A382-A1E8F370A918 |
| p:P5555 | wd:statement/Q6433699-02215d21-476c-6fc0-5534-5a9f7929f61e |
| p:P6104 | wd:statement/Q6433699-7F0E562E-994B-4D43-B023-333DB6D59628 |
| p:P6366 | wd:statement/Q6433699-5636B490-FE06-4F18-9E90-CD911899F49B |
| p:P646 | wd:statement/Q6433699-41CEE16A-ECB7-49FF-BDA6-B4E43DEDD1CB |
| p:P7235 | wd:statement/Q6433699-9628656a-4cd8-ec51-e3ed-33c768f21495 |
| wd:statement/Q6433699-d11ac351-4ab1-6cd1-e8ce-d51a15309504 | |
| wd:statement/Q6433699-d9aa3569-430f-91b1-34fa-b4f2dee56d22 | |
| p:P7554 | wd:statement/Q6433699-fd0dbaca-460d-208e-7844-e44ed4fcd35b |
|
p:direct- |
<https:/ |
| wdt:P138 | Jean-Louis Koszul |
| 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">∈</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false">∨</mo></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mn>0</mn><mo stretchy="false" accent="false">→</mo><msup><mo stretchy="false">⋀</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">→</mo></mrow><mi>d</mi></mover></mrow><msup><mo stretchy="false">⋀</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">−</mo><mn>1</mn></mrow></mrow></msup><mi>E</mi><mo stretchy="false" accent="false">→</mo><mo stretchy="false">⋯</mo><mo stretchy="false" accent="false">→</mo><msup><mo stretchy="false">⋀</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">→</mo></mrow><mi>d</mi></mover></mrow><mi>R</mi><mo stretchy="false" accent="false">→</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">∧</mo><mo stretchy="false">⋯</mo><mo stretchy="false">∧</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">∑</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">−</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">∧</mo><mo stretchy="false">⋯</mo><mo stretchy="false">∧</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">∧</mo><mo stretchy="false">⋯</mo><mo stretchy="false">∧</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 | differential graded-commutative algebra |
| wdt:P31 | mathematical concept |
| wdt:P4215 | "Koszul complex" |
| wdt:P5555 |
<http:/ |
| wdt:P6104 | WikiProject Mathematics |
| 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">∨</mo></mrow></msup></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| wdt:P7554 | "Koszul_complex" |
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