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

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

 PhysOrg.com science news on PhysOrg.com >> Heat-related deaths in Manhattan projected to rise>> Dire outlook despite global warming 'pause': study>> Sea level influenced tropical climate during the last ice age
 Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus So, what did you try already?? (1) shouldn't be too difficult. It's just checking that something is a field...

 Tags extension, field, galois, intermediate field, normal extension
 Thread Tools

 Similar Threads for: Need help proving L is a normal exension of F. Thread Forum Replies Advanced Physics Homework 1 Calculus & Beyond Homework 9 Calculus & Beyond Homework 1 Linear & Abstract Algebra 2 General Physics 0