Determine all the ring homomorphism from $\mathbb{Z}$ to $\mathbb{Q}$ and $\mathbb{Q}$ to $\mathbb{Z}$
My attempt : Ring homomorphism from $\mathbb{Z}$ to $\mathbb{Q}$
Here $\mathbb{Z}$ is cyclic and we know that any ring homomorphism send $1$ to $1$
So $f:\mathbb{Z} \to \mathbb{Q}$ send each integer $n$ to the rational number $\frac{n}{1}$
This implies identity is the only such homomorphism from $\mathbb{Z}$ to $\mathbb{Q}$
But here im confused that how to determine the ring homomorphism from $\mathbb{Q}$ to $\mathbb{Z}?$