Let $M$ be a compact smooth manifold, then it is clear that $C^{\infty}(M)$ is a Frechet algebra with pointwise multiplication and a collection of semi-norm defined by $p_{\alpha}(f):=\sup_{\beta\leq\alpha}||\partial^{\beta}(f)||$.

Now let $M\to N$ be a smooth map between compact smooth manifolds. Then it is clear that $C^{\infty}(M)$ is a Frechet $C^{\infty}(N)$-module.

My question is: is $C^{\infty}(M)$ always a

projectiveFrechet $C^{\infty}(N)$-module?

I think this question is trivial for experts. Please let me know if there is any references or it the question is not suitable for mathoverflow.