Question: What are the automorphisms of Z[x]? I know there are two automorphisms, one of which is the identity map, ø(f(x)) = f(x). What is the other one? ø(f(x)) = -f(x) for all f(x) in Z[x]? Or does it have something to do with the degree or factorization of the polynomials? Please explain in detail because I don't know much about ring automorphisms. Thanks.