Common use of Proposition 1 Clause in Contracts

Proposition 1. 6.22 ([58], Chapter I, Example 2.2(4), Proposition 2.13). Let R, R′ be commutative rings, α : R R′ a ring homomorphism and P, Q two finitely generated projective R-modules. Then HomR(P, Q) ⊗R R′ =∼ HomR' (P ⊗R R′, Q ⊗R R′), (P ⊗R Q) ⊗R R′ ∼= (P ⊗R R′) ⊗R' (Q ⊗R R′), as R′-modules.