Gorenstein ring

commutative Noetherian ring such that, at every prime ideal, the localization has finite injective dimension as a module over itself
Intangible mathematical_concept Q5586177
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Gorenstein ring

Summary

Gorenstein ring is a mathematical concept[1]. It draws 53 Wikipedia views per month (mathematical_concept category, ranking #222 of 1,007).[2]

Key Facts

  • Gorenstein ring is credited with the discovery of Alexander Grothendieck[3].
  • Gorenstein ring's instance of is recorded as mathematical concept[4].
  • Daniel Gorenstein is named after Gorenstein ring[5].
  • Gorenstein ring's subclass of is recorded as Noetherian commutative ring[6].
  • Gorenstein ring's subclass of is recorded as Cohen–Macaulay ring[7].
  • Gorenstein ring's time of discovery or invention is recorded as +1961-00-00T00:00:00Z[8].
  • Gorenstein ring's Freebase ID is recorded as /m/02khhb[9].
  • Gorenstein ring's Stack Exchange tag is recorded as https://math.stackexchange.com/tags/gorenstein[10].
  • Gorenstein ring's defining formula is recorded as \forall\mathfrak p\in\operatorname{Spec}R \colon \operatorname{id}R_{\mathfrak p} < \infty<sup id="cite-C19" class="cite-ref" title="Gorenstein ring — defining formula (P2534): \forall\mathfrak p\in\operatorname{Spec}R \colon \operatorname{id}R_{\mathfrak p} < \infty">[11].
  • Gorenstein ring's MathWorld ID is recorded as GorensteinRing[12].
  • Gorenstein ring's Open Library subject ID is recorded as gorenstein_rings[13].
  • Gorenstein ring's nLab ID is recorded as Gorenstein ring[14].
  • Gorenstein ring's maintained by WikiProject is recorded as WikiProject Mathematics[15].
  • Gorenstein ring's Microsoft Academic ID is recorded as 2775996374[16].
  • Gorenstein ring's in defining formula is recorded as \mathfrak p[17].
  • Gorenstein ring's in defining formula is recorded as R[18].
  • Gorenstein ring's in defining formula is recorded as \operatorname{Spec}[19].
  • Gorenstein ring's in defining formula is recorded as R_{\mathfrak p}[20].
  • Gorenstein ring's Encyclopedia of Mathematics article ID is recorded as Gorenstein_ring[21].

Body

Works and Contributions

Gorenstein ring is credited with the discovery of Alexander Grothendieck[3].

Why It Matters

Gorenstein ring draws 53 Wikipedia views per month (mathematical_concept category, ranking #222 of 1,007).[2] It has Wikipedia articles in 10 language editions, a strong signal of global cultural recognition.[22] It is known by 3 alternative names across languages and contexts.[23]

References

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

Direct Wikidata claims

  1. [4] . wikidata.org.
  2. [3] . wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.
  12. [14] . wikidata.org.
  13. [15] . wikidata.org.
  14. [16] . wikidata.org.
  15. [17] . wikidata.org.
  16. [18] . wikidata.org.
  17. [19] . wikidata.org.
  18. [20] . wikidata.org.
  19. [21] . wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [22] . Wikidata sitelinks. wikidata.org.
  3. [23] . 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). Gorenstein ring. Retrieved May 3, 2026, from https://4ort.xyz/entity/gorenstein-ring
MLA “Gorenstein ring.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/gorenstein-ring.
BibTeX @misc{4ortxyz_gorenstein-ring_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Gorenstein ring}}, year = {2026}, url = {https://4ort.xyz/entity/gorenstein-ring}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Gorenstein ring — https://4ort.xyz/entity/gorenstein-ring (retrieved 2026-05-03)

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