monoid

algebraic structure with an associative operation and an identity element
Thing general Q208237
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monoid

Summary

monoid ranks in the top 2% of general entities by monthly Wikipedia readership (466 views/month).[1]

Key Facts

  • monoid's subclass of is recorded as semigroup[2].
  • monoid's subclass of is recorded as small category[3].
  • monoid's subclass of is recorded as monoid object[4].
  • monoid's subclass of is recorded as unital magma[5].
  • monoid's Commons category is recorded as Monoids[6].
  • monoid's Freebase ID is recorded as /m/04z49[7].
  • monoid's Gran Enciclopèdia Catalana ID is recorded as 0124602[8].
  • monoid's has characteristic is recorded as identity element[9].
  • monoid's has characteristic is recorded as associativity[10].
  • monoid's has characteristic is recorded as closure[11].
  • monoid's defining formula is recorded as \boldsymbol M=\left(M,*,e\right)[12].
  • monoid's studied by is recorded as category theory[13].
  • monoid's MathWorld ID is recorded as Monoid[14].
  • monoid's Treccani ID is recorded as monoide[15].
  • monoid's JSTOR topic ID is recorded as monoids[16].
  • monoid's Open Library subject ID is recorded as monoids[17].
  • monoid's nLab ID is recorded as monoid[18].
  • monoid's Treccani Vocabulary ID is recorded as monoide[19].
  • monoid's maintained by WikiProject is recorded as WikiProject Mathematics[20].
  • monoid's Microsoft Academic ID is recorded as 206901836[21].
  • monoid's ProofWiki ID is recorded as Definition:Monoid[22].
  • monoid's NicoNicoPedia ID is recorded as モノイド[23].
  • monoid's Encyclopedia of Mathematics article ID is recorded as Monoid[24].
  • monoid's PlanetMath ID is recorded as Monoid[25].
  • monoid's Group Properties article ID is recorded as Monoid[26].

Why It Matters

monoid ranks in the top 2% of general entities by monthly Wikipedia readership (466 views/month).[1] monoid has Wikipedia articles in 26 language editions, a strong signal of global cultural recognition.[27] monoid is known by 23 alternative names across languages and contexts.[28]

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] . Freebase Data Dumps. wikidata.org.
  7. [8] . wikidata.org.
  8. [9] . wikidata.org.
  9. [10] . wikidata.org.
  10. [11] . wikidata.org.
  11. [12] . wikidata.org.
  12. [13] . wikidata.org.
  13. [14] . wikidata.org.
  14. [15] . wikidata.org.
  15. [16] . wikidata.org.
  16. [17] . wikidata.org.
  17. [18] . wikidata.org.
  18. [19] . wikidata.org.
  19. [20] . wikidata.org.
  20. [21] . wikidata.org.
  21. [22] . wikidata.org.
  22. [23] . wikidata.org.
  23. [24] . wikidata.org.
  24. [25] . wikidata.org.
  25. [26] . wikidata.org.

Aggregate / graph-position facts

  1. [1] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [27] . Wikidata sitelinks. wikidata.org.
  3. [28] . Wikidata aliases. 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). monoid. Retrieved April 10, 2026, from https://4ort.xyz/entity/monoid
MLA “monoid.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/monoid.
BibTeX @misc{4ortxyz_monoid_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{monoid}}, year = {2026}, url = {https://4ort.xyz/entity/monoid}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): monoid — https://4ort.xyz/entity/monoid (retrieved 2026-04-10)

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