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ordered field

field together with a total ordering of its elements such that the set of positive elements is translation-invariant and multiplicatively closed
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ordered field

Summary

ordered field ranks in the top 2% of general entities by monthly Wikipedia readership (97 views/month).[1]

Key Facts

  • ordered field's subclass of is recorded as ordered ring[2].
  • ordered field's Freebase ID is recorded as /m/05m3v[3].
  • ordered field's Stack Exchange tag is recorded as https://mathoverflow.net/tags/ordered-fields[4].
  • ordered field's Stack Exchange tag is recorded as https://math.stackexchange.com/tags/ordered-fields[5].
  • ordered field's defining formula is recorded as \forall a,b,c\in K\colon(a\le b\implies a+c\le b+c)\land(0\le a\le b\implies 0\le ab)[6].
  • ordered field's studied by is recorded as theory of ordered fields[7].
  • ordered field's nLab ID is recorded as ordered field[8].
  • ordered field's maintained by WikiProject is recorded as WikiProject Mathematics[9].
  • ordered field's Microsoft Academic ID is recorded as 13851312[10].
  • ordered field's in defining formula is recorded as K[11].
  • ordered field's in defining formula is recorded as \le[12].
  • ordered field's in defining formula is recorded as \implies[13].
  • ordered field's in defining formula is recorded as \land[14].
  • ordered field's OpenAlex ID is recorded as C13851312[15].
  • ordered field's underlying structure is recorded as field[16].
  • ordered field's underlying structure is recorded as totally ordered set[17].
  • ordered field's underlying structure is recorded as set[18].
  • ordered field's Metamath statement ID is recorded as df-ofld[19].

Why It Matters

ordered field ranks in the top 2% of general entities by monthly Wikipedia readership (97 views/month).[1] It has Wikipedia articles in 19 language editions, a strong signal of global cultural recognition.[20] It is known by 5 alternative names across languages and contexts.[21]

References

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

Direct Wikidata claims

  1. [2] ↑ . wikidata.org.
  2. [3] ↑ . Freebase Data Dumps. 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.
  10. [11] ↑ . wikidata.org.
  11. [12] ↑ . wikidata.org.
  12. [13] ↑ . wikidata.org.
  13. [14] ↑ . wikidata.org.
  14. [15] ↑ . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.
  15. [16] ↑ . wikidata.org.
  16. [17] ↑ . wikidata.org.
  17. [18] ↑ . wikidata.org.
  18. [19] ↑ . wikidata.org.

Aggregate / graph-position facts

  1. [1] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [20] ↑ . Wikidata sitelinks. wikidata.org.
  3. [21] ↑ . 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). ordered field. Retrieved April 10, 2026, from https://4ort.xyz/entity/ordered-field
MLA “ordered field.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/ordered-field.
BibTeX @misc{4ortxyz_ordered-field_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{ordered field}}, year = {2026}, url = {https://4ort.xyz/entity/ordered-field}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): ordered field — https://4ort.xyz/entity/ordered-field (retrieved 2026-04-10)

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