 In other words, the nonzero elements of "K"/"U" are in one-to-one correspondence with the separable quadratic extension fields of "K".So the Arf invariant of a nonsingular quadratic form over "K" is either zero or it describes a separable quadratic extension field of "K".This is analogous to the discriminant of a nonsingular quadratic form over a field "F" of characteristic not 2.