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Math Help - Non-trivial homomorphism

  1. #1
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    Non-trivial homomorphism

    Let f:R \rightarrow R a non-trivial ring homomorphism.

    Prove:

    a) f(Q) \subset and  f|_Q = id_Q
    b) if a > b then f(a) > f(b)
    c) f is smooth. Deduce that f=id_R

    Thanks!
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    Maybe this helps?
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