Thread: Extension Field

1.Let F be an extension field of K and let u be in F. Show that K(a^2)contained in K(a) and [K(u):K(a^2)]=1 or 2.

2.Let F be an extension field of K and let a be in F be algebraic over K with minimal polynomial m(x). Show that if degm(x) is odd then K(u)=K(a^2).



Ideas:
1.I was thinking of looking at [K(u):K(a)][K(a):K(a^2)]

2.Well I know if a, is algebraic, then there exists a minimal polynomial m(x) such that m(a)=0. The degrees is what confuses me

These two I am getting nowhere with. Am I on the right track or is there a better direction to go?

2. I was thinking of somehow using a theorem stating [F:K]=[F:K(u)][K(u):K]
based on the deg m(x) being odd, I would say deg m(x)=2n+1

What is u in problem one？