let k be a field.
a) show that the mapping definded by for fixed is an automorphism of k[t] which is the identity on k.
b) conversely, let be an automorphism of k[t] which is the identity on k. Prove that thre exist with such that as in part a)
So I have done part a) but I can't seem to get out of the gate for part b).
I keep reading the problem and only seeing the trivial solution.
The identitiy map is an automorphism so and satisfy the above, but I have a feeling that is not what Dummit and Foote had in mind.
A push in the right direction would be great.