Proposition 9

The A-homomorphism $f'' = \varprojlim f''_\alpha : \varprojlim \Lambda_{A_\alpha}(M_\alpha) \to \Lambda_A(M)$ is a graded algebra isomorphism.

The proof is the same as that of § 5, no. 4, Proposition 6 replacing throughout T by $\Lambda$ and $\phi$ by $\phi''$ and taking account of the fact that a direct limit of alternating algebras is alternating.