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Math Help - Ring Homomorphism

  1. #1
    Junior Member
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    Ring Homomorphism

    Show that the identity mapping is the only ring homomorphism from Z into Z.

    I know that:
    Ring homomorphism exsits if there is a function φ: RS such that the following are true:
    i) φ(a+b) = φ(a) + φ(b)
    ii) φ(ab) = φ(a)φ(b)
    iii) φ(1) = 1
    Identity mapping maps each element of R to itself, and is always bijective.

    I need help writing the proof of this. Thanks ahead of time.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Hint

    \varphi (2)=\varphi (1+1)=\varphi(1)+\varphi (1)=1+1=2

    Try to generalize for n\in\mathbb{Z} .
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