Do we know anything about all possible degree 3 field extensions?
If characteristic is 3:
If Galois, then Artin-Schreier.
If inseparable, then this is just cube root.
If separable, but not normal, then what???
If characteristic is not 3 (automatically separable):
If Galois, then this come from adjoining a cube root or not? (some people told me yes, some no)
What if non-Galois?
Anyone know the answer to these? Thanks.