I am a bit confused with terminology. I know that "the subfield of $E/F$ generated by $S$" means $F(S)$ (the subfield of $E$ generated by $F$ and $S$), and "the subring of $E/F$ generated by $S$" is the subring of $E$ generated by $F$ and $S$.
Though in my book it was never explicitly stated what "subring of $E/F$" or "subfield of $E/F$" means. Can someone please explicitly state the meaning of the two?
A subring of $E/F$ is just a ring $R$ such that $F \subseteq R \subseteq E$. Also called an intermediary ring.
A subfield of $E/F$ is just a field $K$ such that $F \subseteq K \subseteq E$. Also called an intermediary field.