Hi. Can you verify if I'm right?

(normal/normal)

(not normal/normal)

(normal/not normal)

(not normal/not normal)

Now assume is a normal extention over and

is normal over iff given an algebraic closure of any -isomorphism from to another subfield of is a -automorphism of Since a -isomorphism from to another subfield of is also a -isomorphism, then it is a -automorphism of and is a normal extension over

Finally, consider:

is a normal extension, but what about and ?