Finite integral domain

Question

I encountered a problem:

Every finite integral domain is isomorphic to $ \mathbb{ Z }_{p} $.

I know that finite integral domain is isomorphic to a field, but I have no idea on how to construct a homomorphism to $\mathbb{Z}_{p}$ (or maybe it is wrong, but I haven come up with a counterexample).

Answer 1

Thanks to @shery and @lhf, the conterexamples come from their comments.

A finite integral domain which actually is a (finite) field will have the order of the form ${p}^{n}$, where $p$ is a prime. Then when $n>1$, it is not isomorphic to $\mathbb{Z}_{{p}^{n}}$ since $\mathbb{Z}_{{p}^{n}}$ is not a field.