Galois extension
If "K"/"F" is a Galois extension and "x" in "E" generates a normal basis over "F", then "x" is free in "K"/"F". If "x" has the property that for every subgroup "H" of the Galois group "G", with fixed field "K""H", "x" is free for "K"/"K""H", then "x" is said to be completely free in "K"/"F". Every Galois extension has a completely free element.