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commutative ring

algebraic structure
Thing general Q858656
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commutative ring

Summary

commutative ring ranks in the top 2% of general entities by monthly Wikipedia readership (249 views/month).[1]

Key Facts

  • commutative ring is a type of graded-commutative ring[2].
  • commutative ring is a type of polynomial identity ring[3].
  • commutative ring's said to be the same as is recorded as affine scheme[4].
  • commutative ring is the opposite of noncommutative ring[5].
  • commutative ring comprises abelian group[6].
  • commutative ring comprises commutative monoid[7].
  • commutative ring's studied by is recorded as commutative algebra[8].
  • commutative ring's on focus list of Wikimedia project is recorded as Wikipedia:Vital articles/Level/4[9].
  • commutative ring's maintained by WikiProject is recorded as WikiProject Mathematics[10].

Body

Definition and Type

Recorded subclass of include graded-commutative ring[2] and polynomial identity ring[3]. It is the opposite of noncommutative ring[5].

Use and Application

Components include abelian group[6], a mathematical concept[11] and commutative monoid[7].

Why It Matters

commutative ring ranks in the top 2% of general entities by monthly Wikipedia readership (249 views/month).[1] It has Wikipedia articles in 24 language editions, a strong signal of global cultural recognition.[12] It is known by 13 alternative names across languages and contexts.[13]

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.
  7. [8] ↑ . wikidata.org.
  8. [9] ↑ . wikidata.org.
  9. [10] ↑ . wikidata.org.

Inline context (facts about related entities)

  1. [11] ↑ . Wikidata. wikidata.org. → on this site

Aggregate / graph-position facts

  1. [1] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [12] ↑ . Wikidata sitelinks. wikidata.org.
  3. [13] ↑ . 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). commutative ring. Retrieved April 11, 2026, from https://4ort.xyz/entity/commutative-ring
MLA “commutative ring.” 4ort.xyz Knowledge Graph, 4ort.xyz, 11 Apr. 2026, https://4ort.xyz/entity/commutative-ring.
BibTeX @misc{4ortxyz_commutative-ring_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{commutative ring}}, year = {2026}, url = {https://4ort.xyz/entity/commutative-ring}, note = {Accessed: 2026-04-11}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): commutative ring — https://4ort.xyz/entity/commutative-ring (retrieved 2026-04-11)

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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. 9d ago · 慈居 · 2026-05-12 view diff on Wikidata ↗
    Subclass of → —
    Maintained by wikiproject → WikiProject Mathematics
    Studied by → commutative algebra
    Said to be the same as → affine scheme
    + 6 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-create:2||1 */ [[Property:P279]]: [[Q7595790]]"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.