Let K be a finite extension of a field F such that for every two intermediate field $M_1$, $M_2$ we have $M_1\subset M_2$ or $M_2\subset M_1$. I need to show that there is an element $a\in K$ such that $K=F(a)$.
I have an idea that goes like this: If I show that there are finite intermediate fields, then I could use the Primitive Element Theorem (which demonstration wasn't given during my algebra course, so I would have to include this in my solution so it can be whole).
There's also some doubts here: through the internet we can see that some people enunciate the Primitive Element theorem excluding the hypothesis of the extension (finite) having finite intermediate subfields. Which one is the correct?