So I have an exercise that I'm not sure what is being asked to accomplish. It states:
If $f:\Bbb Z \to \Bbb Z$ is a morphism of rings with unity (i.e. a morphism of rings such that $f(1)=1$), then $f$ is the identity.
This seems to me to be more of a statement than a question. I'm new to abstract algebra so what the goal here might be obvious for more experienced mathematicians despite the badly worded problem. If anyone could point me in the right direction that would be greatly appreciated.
You have $f(n)=f(n.1)=f(1+...+1)$ Where $1+....1$ represents the addition of $1$ $n$-times, you deduce that $f(1)=nf(1)$ since $f(x+y)=f(x)+f(y)$ so $f(n)=n$.