# Need help proving L is a normal exension of F.

1. Nov 26, 2011

### ae1709

Let

{F}\subseteq{K_i}\subseteq{E}

for i = 1,...,r with E a finite extension of F and where the intermediate fields $$K_i$$are each normal extensions of F for all i.

Define:

L = \{f(a_1,....,a_r) : [f]\in{F[x]}, [a_i]\in[K_i]\}

1) Prove that L is a subfield of E and contains $$K_i$$ for all i.

2) Prove that L is a normal extension of F.

I really need help with this. Thanks

2. Nov 28, 2011

### micromass

So, what did you try already?? (1) shouldn't be too difficult. It's just checking that something is a field...