Assume that $E\subset F$ and that $E$ and $F$ are fields. Also, say $[E:F]=p$, where $p$ is a prime. If $a$ is any element of $F\setminus E$. Show that $F=E(a)$.
I'm pretty unsure of how to approach this.
Assume that $E\subset F$ and that $E$ and $F$ are fields. Also, say $[E:F]=p$, where $p$ is a prime. If $a$ is any element of $F\setminus E$. Show that $F=E(a)$.
I'm pretty unsure of how to approach this.