Question regarding the definition of intermediate field

Question

Say I have a field extension $L\supset K$. My question is whether $L$ and $K$ themselves are considered intermediate fields, i.e. whether the inclusions in a tower $L\supset M\supset K$ have to be strict for $M$ to be considered an intermediate field.

Answer 1

Like Dietrich Burde already mentioned in the comments, one usually defines an intermediate field $M$ of a field extension $L/K$ to be a field such that $K \subseteq M \subseteq L$. Though, some authors might use $\subset$ for $\subseteq$ and $\subsetneq$ for $\subset$.