Is $\mathbb Z _p$ flat $\mathbb Z$-module?

Question

Is $\mathbb Z _p$ flat $\mathbb Z$-module?

$\mathbb Z/n \mathbb Z $ is not flat over $\mathbb Z$, so I guess it's inverse limit $\mathbb Z /p^m\mathbb Z$ is not flat. But I'm not confident.

Thank you in advance.

Answer 1

Yes, because it is torsion-free ($\mathbb{Z}$-module is flat iff it is torsion free). A similar question was asked here