Consider the ring $\mathbb{Z}_p[[X]] \otimes_\mathbb{Z} \mathbb{Q}_p$ and the ideal generated by $(X-p)^r$ (for some integer $r$).
Is the following true : for all integer $r$, the ring $ \frac{\mathbb{Z}_p[[X]] \otimes_\mathbb{Z} \mathbb{Q}_p}{(X-p)^r} $ is principal ?
I can see that for $r=1$, the ring is isomorphic to $\mathbb{Q_p}$ (so it is principal), but I don't know when $r \geq 2$.