# abstract algebra – Ring of Endomorphism over \$mathbb{Z}_n\$

I must have some definition problem which I can’t put my finger on:
When defining homomorphism of rings $$f :R mapsto S$$, we require:
$$f(1_R)=1_s$$
$$f(r_1+r_2)=f(r_1)+f(r_2)$$
Now I have question asks to prove that End($$mathbb{Z}_n$$) isomorphic to $$mathbb{Z}_n$$. If every endomorphism $$f$$ must send 1 to itself, and preserve sum, how can I get 2 different enomorphisms?