Exercise 6, § 7

Let $k$ be a ring, $A$ a linearly topologized formally smooth $k$-algebra. Prove that for every open ideal $J$ of $A$, the $A/J$-module $(A/J) \otimes_A \Omega_k(A)$ is projective (prove, using the example of No. 1, that for every surjective homomorphism of $A/J$-modules $M \to M''$, every $k$-derivation of $A$ into $M''$ lifts to $M$).