Let $K$ be a field of characteristic $p$. Show that there is a unique ring homomorphism $\mathbb{F}_p\to K$.

Question

Let $p$ be a prime number and $\mathbb F_p = \mathbb Z/p\mathbb Z$ be the field with $p$ elements. Let $K$ be a field of characteristic $p$. Show that there is a unique ring homomorphism $\mathbb{F}_p\to K$.

I have no idea where to start! :(

Answer 1

Well, we know that $1$ should go to $1$. This means that $1+1$ should go to $1+1$, and so on. This will determine the homomorphism.