Corollary 3
Tag 0D3H, permanent. Cite it as [Bourbaki, Tag 0D3H].
Commutative Algebra, chapter X, § 2. Modules et anneaux macaulayens
Let A be a noetherian ring, B a finite flat Λ-algebra, M a finitely generated Macaulay A-module. Then the B-module M ⊗_A B is a Macaulay module.
In fact, for every p ∈ Spec(A), the ring κ(p) ⊗_Λ B is a finite κ(p)-algebra, hence is a Macaulay ring (No. 5, example 1), and we apply prop. 9.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
Nothing.
Cites
Nothing.