Let L be a finitely generated extension of a field K having characteristic p ≠ 0. A rank t higher derivation on L over K is a sequence
of additive maps of K into K such that
d0 is the identity map and dt(x) = 0, i > 0, x ∊ K.  contains the relevant background material on higher derivations. By Zorn's Lemma, there are maximal separable extensions of K in L. A maximal separable extension D of K in L is called distinguished if
Dieudonné  established that any finitely generated extension always has distinguished subfields. L has the same dimension over any distinguished subfield , and this dimension is called the order of inseparability of L/K. The least n such that K(LP)n is separable over K is called the inseparable exponent of L/K, inex(L/K).