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prime ideal

ideal such that, whenever a product belongs to it, at least one of its factors also belong to it
Thing general Q863912
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prime ideal

Summary

prime ideal ranks in the top 2% of general entities by monthly Wikipedia readership (449 views/month).[1]

Key Facts

  • prime number is named after prime ideal[2].
  • prime ideal is a type of primary ideal[3].
  • prime ideal is a type of irreducible ideal[4].
  • prime ideal's topic's main category is recorded as Category:Prime ideals[5].
  • prime ideal's facet of is recorded as prime element[6].
  • prime ideal's different from is recorded as irreducible ideal[7].
  • prime ideal's different from is recorded as prime ideal[8].
  • prime ideal's maintained by WikiProject is recorded as WikiProject Mathematics[9].

Body

Definition and Type

Recorded subclass of include primary ideal[3] and irreducible ideal[4].

Origins

prime number is named after prime ideal[2].

Why It Matters

prime ideal ranks in the top 2% of general entities by monthly Wikipedia readership (449 views/month).[1] It has Wikipedia articles in 21 language editions, a strong signal of global cultural recognition.[10] It is known by 7 alternative names across languages and contexts.[11]

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.

Aggregate / graph-position facts

  1. [1] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [10] ↑ . Wikidata sitelinks. wikidata.org.
  3. [11] ↑ . 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). prime ideal. Retrieved April 10, 2026, from https://4ort.xyz/entity/prime-ideal
MLA “prime ideal.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/prime-ideal.
BibTeX @misc{4ortxyz_prime-ideal_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{prime ideal}}, year = {2026}, url = {https://4ort.xyz/entity/prime-ideal}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): prime ideal — https://4ort.xyz/entity/prime-ideal (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. 8d ago · Bezik · 2026-05-25 view diff on Wikidata ↗
    Different from → irreducible ideal, prime ideal
    "/* wbsetclaim-update:2||1 */ [[Property:P1889]]: [[Q139919115]]"
  2. 29d ago · MatSuBot bot · 2026-05-04 view diff on Wikidata ↗
    Facet of → prime element
    Subclass of → primary ideal, irreducible ideal
    Named after → —
    Topic's main category → Category:Prime ideals
    + 5 other properties edited (see Wikidata diff for full list)
    "/* wbeditentity-update-languages-short:0||my, eo */ import labels from sitelinks; cleanup"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.