Hi, I'm having problems with the second part of this problem.
Let be an extension of and transcendental over .
Let with . Show:
a) is transcendental over .
b) If and , then is transcendental over .
For part a, I assumed otherwise, so there exists a such that , but and which contradicts being transcendental over .
For part b, I'm not sure. I tried doing it by contradiction also, but I'm not getting anywhere. I feel like it's relatively simple, and I'm just forgetting something obvious. Any help would be appreciated! Thanks!