Studying a prime field, Prime fields has no proper subfields.
At this point, i have some question.
Suppose that $F$ is a field and $E$ is an extension of $F$. Suppose further that there is no intermediate field between $F$ and $E$.
Then, is it true that
1) Both $F$ and $E$ equals some prime fields?
2) $E$ is a simple extension of $F$?
or is there an extension of $F$ of degree infinite?
Give some advice. Thank you!