Let R be the reals , denote A:=C^{\infty} (R) the ring of smooth
functions defined on R ( with real values).
Prove (or disprove) the existence of an A module V and a derivation
d: A --> V such that
d(e^x) not= e^x dx
I've seen the claim of existence, without a proof, in some course notes
Related to this :
Show that the module of differentials ( universal derivations)
of A over R is not ( is ) the A module of differential 1 forms on R.
More general for A :=C{\infty} (M) , M manifold.
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