1.Let F=K(u) where u is transcedental over the field K. If E is a field such that K contained in E contained in F, then Show that u is algebraic over E.
Let a
be any element of E that is not in K. Then a = f(u)/g(u)
for some polynomials f(x), g(x) inK[x]
2.Let F be a finite extension of K such that [F:K]=p, a prime number. If u in F but u not in K, show that F=K(u)
I'm not quite sure how to get started on this one
3.Let K contained in E contained in F be fields. Prove that if F is algebraic over K, then F is algebraic over E and E is algebraic over K
F is algebraic so F(u)=0
We want to show E(u)=0