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Polynomial ring automorphisms

  1. May 18, 2014 #1
    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.
     
  2. jcsd
  3. May 18, 2014 #2
    Close: Try ##\phi## given by ##\phi(f)(x)=f(-x)##.

    More generally, if ##R## is any commutative ring, and ##u\in R## is any unit element, then ##\phi_u## given by ##\phi_u(f)(x)=f(ux)## is a ring automorphism.
     
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