Proposition 8

The $A$-homomorphism $f' = \lim \rightarrow f'_\alpha : \lim \rightarrow S_{A_\alpha}(M_\alpha) \to S_A(M)$ is a graded algebra isomorphism.

The proof is the same as that of § 5, no. 5, Proposition 6 replacing throughout $T$ by $S$ and $\phi$ by $\phi'$ and taking account of the fact that a direct limit of commutative algebras is commutative.