Bourbaki

Remark 2

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

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

Every quotient ring of a catenary ring is catenary. In order that the ring A be catenary, it is necessary and sufficient that, for every prime ideal p of A, the ring ApA_p be catenary.

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

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