Corollary 2

Let ρ : A → B be a homomorphism of noetherian rings making B into a faithfully flat A-module and let M be a finitely generated A-module. In order that the B-module M ⊗_A B be a Macaulay module, it is necessary and sufficient that the A-module M be a Macaulay module and that κ(p) ⊗_Λ B be a Macaulay ring for every p ∈ Supp(M).