No sub-integral domain of Z with prime characteristic?

Question

I try to find a subring of Z which it is integral domain and characteristic is a prime. Until now, I can't find it. But i believe that this proposition is true. Please help me prove or disprove.

Answer 1

$\mathbb{Z}$ has characteristic $0$. Hence, every subring of $\mathbb{Z}$ also has characteristic zero. But the only subring is $\mathbb{Z}$ anyway. (If you work in the category of non-unital rings, then $0$ is another subring and this has characteristic $1$.)