Well, it's an automorphism with respect to addition...
(sighs) I need someone to confirm if I'm going insane again.
If it's an automorphism then it's a homomorphism. But:Prove that for each fixed nonzero the map from to itself by is an automorphism of .
is not a homomorphism, except for k = 1:
What am I missing this time? (It's just been that kind of day.)