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projective module

in algebra, a module that is the direct summand of a free module
Thing general Q942423
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projective module

Summary

projective module has Wikipedia articles in 12 language editions, a strong signal of global cultural recognition.[1]

Key Facts

  • projective module is a type of flat module[2].
  • projective module is a type of projective object[3].
  • projective module is the opposite of injective module[4].
  • projective module's Stack Exchange tag is recorded as https://mathoverflow.net/tags/projective-modules[5].
  • projective module's studied by is recorded as module theory[6].
  • projective module's maintained by WikiProject is recorded as WikiProject Mathematics[7].

Body

Definition and Type

Recorded subclass of include flat module[2] and projective object[3]. projective module is the opposite of injective module[4].

Why It Matters

projective module has Wikipedia articles in 12 language editions, a strong signal of global cultural recognition.[1]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [2] ↑ . wikidata.org.
  2. [3] ↑ . wikidata.org.
  3. [4] ↑ . wikidata.org.
  4. [5] ↑ . wikidata.org.
  5. [6] ↑ . wikidata.org.
  6. [7] ↑ . wikidata.org.

Aggregate / graph-position facts

  1. [1] ↑ . Wikidata sitelinks. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). projective module. Retrieved April 10, 2026, from https://4ort.xyz/entity/projective-module
MLA “projective module.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/projective-module.
BibTeX @misc{4ortxyz_projective-module_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{projective module}}, year = {2026}, url = {https://4ort.xyz/entity/projective-module}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): projective module — https://4ort.xyz/entity/projective-module (retrieved 2026-04-10)

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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 2d ago · Mynus grey · 2026-07-02 view diff on Wikidata ↗
    P14534 → Module.Projective
    "/* wbcreateclaim-create:1| */ [[Property:P14534]]: Module.Projective, #quickstatements; #temporary_batch_1783013068346"
  2. 12d ago · HTinC23 · 2026-06-23 view diff on Wikidata ↗
    P14540 → Q2716519
    Opposite of → injective module
    "/* wbeditentity-statements-multiple-properties-update:0||2 */ Moving [[Property:P461]] to [[Property:P14540]]"
  3. 5w ago · Twofivesixbot bot · 2026-05-26 view diff on Wikidata ↗
    Opposite of → injective module
    Subclass of → —
    Maintained by wikiproject → WikiProject Mathematics
    Aliases → —
    + 2 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-update-qualifiers:1||1|2 */ [[Property:P8189]]: 987007538596705171, mv to monolingual text names on J9U statements"
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