Definition 7

Tag 0CKB, permanent. Cite it as [Bourbaki, Tag 0CKB].

Commutative Algebra, chapter VIII, § 1. Dimension de Krull d’un anneau

A ring A is said to be catenary if the topological space Spec(A) is catenary (No. 2, Definition 4).

This therefore means that, for every pair (p, q) of prime ideals of A such that $q \subset p$ , all saturated chains of prime ideals of A with endpoints p and q have length $\operatorname{codim}(V(p), V(q)) = \dim(A_p/qA_p)$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Nothing.