catenary ring

commutative ring admitting a good dimension function, i.e. that relative dimension between two prime ideals is well defined, in the sense that any maximal strictly increasing chain of prime ideals between the two has the same finite length
Thing general Q5051871
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catenary ring

Summary

catenary ring ranks in the top 2% of general entities by monthly Wikipedia readership (14 views/month).[1]

Key Facts

  • catenary ring's subclass of is recorded as commutative ring[2].
  • catenary ring's subclass of is recorded as noetherian ring[3].
  • catenary ring's Freebase ID is recorded as /m/02p_hs_[4].
  • catenary ring's defining formula is recorded as \forall p_0,\dotsc, p_m, q_0,\dotsc, q_n\in\operatorname{Spec}R\colon( p_0= q_0)\land( p_m= q_n)\land( p_0\subsetneq p_1\subsetneq\dotsb\subsetneq p_m)\land( q_0\subsetneq q_1\subsetneq\dotsb\subsetneq q_n)\land\left(\forall i\nexists p'\colon p_i\subsetneq p'\subsetneq p_{i+1}\right)\land\left(\forall j\nexists q'\colon q_j\subsetneq q'\subsetneq q_{j+1}\right)\implies m=n[5].
  • catenary ring's BabelNet ID is recorded as 00121015n[6].
  • catenary ring's maintained by WikiProject is recorded as WikiProject Mathematics[7].
  • catenary ring's Microsoft Academic ID is recorded as 2781019547[8].

Why It Matters

catenary ring ranks in the top 2% of general entities by monthly Wikipedia readership (14 views/month).[1] It has Wikipedia articles in 8 language editions, a strong signal of global cultural recognition.[9]

📑 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). catenary ring. Retrieved April 10, 2026, from https://4ort.xyz/entity/catenary-ring
MLA “catenary ring.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/catenary-ring.
BibTeX @misc{4ortxyz_catenary-ring_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{catenary ring}}, year = {2026}, url = {https://4ort.xyz/entity/catenary-ring}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): catenary ring — https://4ort.xyz/entity/catenary-ring (retrieved 2026-04-10)

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