SHMARQL

projective module

<http://www.wikidata.org/entity/Q942423>

in algebra, a module that is the direct summand of a free module
rdfs:label
"projective module"@en
skos:altLabel "有限生成射影加群"@ja
schema:description
"in algebra, a module that is the direct summand of a free module"@en
schema:dateModified "2026-09-06T20:28:37+00:00"^^xsd:dateTime
schema:version 2541300182
wikibase:identifiers 15
wikibase:sitelinks 12
wikibase:statements 31
p:P10037 wd:statement/Q942423-e2ce5ec5-4f2d-fb39-0b8e-2991a22faaa8
p:P10283 wd:statement/Q942423-4DE3F38A-0AF8-47EF-9724-674DA64A9341
p:P10376 wd:statement/Q942423-d0ed9531-4f65-4ec6-1adb-c44736515f63
p:P13591 wd:statement/Q942423-E5C7C251-520C-4F90-83DE-542AFAA7EAFB
p:P14534 wd:statement/Q942423-E59C336D-C7F1-4482-BD5E-4CD055356759
p:P14540 wd:statement/Q942423-A96BE4AD-6BBC-4E07-924E-997C2CABA8F8
p:P1482 wd:statement/Q942423-44eddfc0-407c-a906-0946-8595dcc7eee6
p:P227 wd:statement/Q942423-2733ed9c-4584-20c3-20cc-f2bd69882ef3
p:P244 wd:statement/Q942423-B4CA21B6-54D8-49A1-BAC3-8975379D85AE
p:P2534 wd:statement/Q942423-6B4309A3-D2A1-4D96-ACAA-FC1F0DF86807
p:P2579 wd:statement/Q942423-5C30BC84-4785-4617-B2A6-68D2DF1AF518
p:P279 wd:statement/Q942423-9227ed02-4b5c-e2cd-3369-3688eab39fbd
wd:statement/Q942423-e0b5f866-4809-8b52-80fc-67f18ae31c64
p:P2812 wd:statement/Q942423-1C7E4FEC-DAAB-4D92-A4DB-3C178C5116BE
p:P4215 wd:statement/Q942423-23342CFB-D0D7-4F37-9BA7-7A8AF6DF0851
p:P5555 wd:statement/Q942423-4191ba9f-43f0-c33f-229a-9300114192eb
p:P6104 wd:statement/Q942423-D5F8EFFF-C098-424D-84F3-9AC44A626713
p:P6366 wd:statement/Q942423-4E16D6DD-1F92-4B6B-BC75-A52FD4FC0482
p:P646 wd:statement/Q942423-2D78A37B-1B93-4B6D-AAF5-343F44A4E847
p:P6781 wd:statement/Q942423-75b6cefa-4b73-f18a-41ad-13a12c485193
p:P7235 wd:statement/Q942423-15db9db6-491d-a61b-6db9-ad3a5508a46b
wd:statement/Q942423-1e2e32af-4c04-cb96-1ad9-344ebaf94ae2
wd:statement/Q942423-ab545159-45c8-18ef-183b-c1f601c38347
wd:statement/Q942423-b1ff206b-4bc0-78fd-69da-464aedcc1d52
wd:statement/Q942423-b96ac463-40ee-d3aa-1516-c8f8a27ff4d6
wd:statement/Q942423-cfd40efc-49a5-fae0-95b7-e1ab49110b0c
wd:statement/Q942423-f588a929-47c3-4a59-2f9f-79fff6da6ff8
wd:statement/Q942423-f89840a7-4bcb-5980-d604-d7a35f6c7165
p:P7554 wd:statement/Q942423-2C4CD0ED-5567-4E4A-9847-7AE9F19B4EE3
p:P7726 wd:statement/Q942423-58547813-491f-04d1-1ccf-07df877edc2c
p:P8189 wd:statement/Q942423-8C32E2ED-F25F-4457-A906-8425951F1D3B
p:direct-normalized/P227 <https://d-nb.info/gnd/4175892-4>
p:direct-normalized/P244 <http://id.loc.gov/authorities/names/sh85107381>
p:direct-normalized/P6366 <https://makg.org/entity/32268108>
wdt:P10037 "modulo-proiettivo"
wdt:P10283 "C32268108"
wdt:P10376 "mathematics/projective-module"
wdt:P13591 "concept/d2e7697c-c424-4bf4-add4-cefda2feb0ac"
wdt:P14534 "Module.Projective"
wdt:P14540 injective module
wdt:P1482 <https://mathoverflow.net/tags/projective-modules>
wdt:P227 "4175892-4"
wdt:P244 "sh85107381"
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"><mi>P</mi><mo stretchy="false">&#x2208;</mo><msub><mi data-mjx-texclass="OP" mathvariant="normal">ProjMod</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>&#x27FA;</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi mathvariant="normal">&#x2203;</mi><mi>Q</mi><mo stretchy="false">&#x2208;</mo><msub><mi data-mjx-texclass="OP" mathvariant="normal">Mod</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub><mi mathvariant="normal">&#x2203;</mi><mi>&#x03BA;</mi><mo stretchy="false">&#x2208;</mo><mi data-mjx-texclass="OP" mathvariant="normal">Card</mi><mo>&#x2061;</mo><mo stretchy="false">&#x003A;</mo><mi>P</mi><mo stretchy="false">&#x2295;</mo><mi>Q</mi><mo stretchy="false">&#x2245;</mo><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">&#x2295;</mo><mi>&#x03BA;</mi></mrow></mrow></msup></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P2579 module theory
wdt:P279 flat module
projective object
wdt:P2812 "ProjectiveModule"
wdt:P4215 "projective module"
wdt:P5555 <http://commons.wikimedia.org/wiki/Special:FilePath/Projective%20module.png>
wdt:P6104 WikiProject Mathematics
wdt:P6366 "32268108"
wdt:P646 "/m/01_ty9"
wdt:P6781 "Definition:Projective_Module"
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>&#x03BA;</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>P</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>Q</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"><mo stretchy="false">&#x2245;</mo></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"><mo stretchy="false">&#x2295;</mo></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"><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>&#x27FA;</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle></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>R</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">&#x2295;</mo><mi>&#x03BA;</mi></mrow></mrow></msup></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P7554 "Projective_module"
wdt:P7726 "ProjectiveModule"
wdt:P8189 "987007538596705171"
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