This is a slight variant of a [question](https://math.stackexchange.com/questions/426376/the-action-of-a-galois-group-on-a-prime-ideal-in-a-dedekind-domain) I asked earlier. 

Let $A$ be a commutative Dedekind domain and $K$ its field of fractions. Let $L/K$ be a finite Galois extension with Galois group $G$ and let $B$ be the integral closure of $A$ in $L$. 

If $\frak{P}$ is a non-zero prime (maximal) ideal of $B$ is it true that as $\sigma$ runs through $G$ the prime ideals $\sigma\frak{P}$ of $B$ are all COPRIME? If so, why? 

Help would again be very much appreciated.