I have the following question. Is the quotient of a dedekind domain A in a numberfield K by a prime I always a perfect field? I understand it for the ring of integers in a finite (separable) extension K of $\mathbb{Q}$ because it is a free $\mathbb{Z}$-module of finite rank. Maybe someone can help me. :)
EDIT: First of all i see that $\mathbb{Z} \subseteq A$ and that $I\cap \mathbb{Z}$ is a (nonzero) primeideal (p). So I see $\mathbb{F}_p \subseteq A/I$. does it help?