Looks good to me.
You can tell the second is not normal because the other two roots are imaginary and . But yeah I think you got it.
Just trying to get my head around normal extensions.
True or False?
is a normal extension of
is a normal extension of
I would say for the first one, true, because it is the splitting field of .
For the second one, false, because is irreducible by Eisenstein, and has only one zero > 0 in
Could anyone please tell me if these are OK?
Thanks in advance!