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Is the map $f: \mathbb C \to \mathbb Z$, $f(a+bi)=a$, for $a,b$ in $\mathbb Z$, a homomorphism of rings?

Any one could give me some ideas please?

  • 3
    It seems like the domain of this function is really the gaussian integers $\mathbb{Z}[i]$, and not all of $\mathbb{C}$2012-03-25

3 Answers 3