  We show that a formal power series ring $A[[X]]$ over a noetherian ring $A$
is not a projective module unless $A$ is artinian. However, if $(A,{\mathfrak
m})$ is local, then $A[[X]]$ behaves like a projective module in the sense that
$Ext^p_A(A[[X]], M)=0$ for all ${\mathfrak m}$-adically complete $A$-modules.
The latter result is shown more generally for any flat $A$-module $B$ instead
of $A[[X]]$. We apply the results to the (analytic) Hochschild cohomology over
complete noetherian rings.
