I'm struggling with this question:
Let us consider $\mathbb{F}_9$. Is it true that a primitive 3rd root of the unit over $\mathbb{F}_3$ is contained in $\mathbb{F}_9$?
I just know that $x=1$ is a root of course of $x^3-1$ over $\mathbb{F}_3$. I can't find its splitting field because $3$ is not coprime with $3$. I really don't know how to move in order to answer the question