Definition 10.104.1. A ring $R$ is said to be catenary if for any pair of prime ideals $\mathfrak p \subset \mathfrak q$, all maximal chains of primes $\mathfrak p = \mathfrak p_0 \subset \mathfrak p_1 \subset \ldots \subset \mathfrak p_ e = \mathfrak q$ have the same (finite) length.
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