$(\Bbb Z/p^k\Bbb Z)\otimes \Bbb F\simeq \Bbb F$ for characteristic $p$ field $\Bbb F$?

Question

In the comment of this post, it says that $(\Bbb Z/p^k\Bbb Z)\otimes \Bbb F\simeq \Bbb F$, where $\Bbb F$ is a characteristic $p$ field. But I don't understand why it's true. Could somebody explain about this?

Answer 1

Basically, for any abelian group $A$, $(\mathbb{Z}/p^k\mathbb{Z})\otimes_{\mathbb{Z}} A\simeq A/p^kA$. Is that something that makes sense to you?

Because then when $A=\mathbb{F}$ is a field of characteristic $p$, $p\mathbb{F}=0$ so $\mathbb{F}/p^k\mathbb{F}\simeq \mathbb{F}$.