Prove that if L/G and G/F are separable algebraic extensions (not necessarily finite), then L/F is also separable.
I could do it for the finite case, but I'm not sure what to do here?
Prove that if L/G and G/F are separable algebraic extensions (not necessarily finite), then L/F is also separable.
I could do it for the finite case, but I'm not sure what to do here?
Ohh I'm sorry, that should have said, "if L/G and G/F are *separable* algebraic extensions".
And we already proved in class that if L/G and G/F are both algebraic extensions (not necessarily finite) then L/F is an algebraic extension. So I just need to show L/F is separable too.