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
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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]