Corollary 3
Tag 0D3M, permanent. Cite it as [Bourbaki, Tag 0D3M].
Commutative Algebra, chapter X, § 2. Modules et anneaux macaulayens
Every algebra of finite type over a noetherian Macaulay ring is catenary.
For such an algebra is a quotient of a polynomial ring over a Macaulay ring, hence a quotient of a Macaulay ring (cor. 2), and therefore is catenary (No. 2).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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