# Math Help - Ring Homomorphism

1. ## 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: RàS 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.

2. Hint

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

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