Geodesic
Higher Derivations and Distinguished Subfields
Canadian journal of mathematics, Tome 40 (1988) no. 1, pp. 131-141

Voir la notice de l'article provenant de la source Cambridge University Press

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 d 0 is the identity map and dt(x) = 0, i > 0, x ∊ K. [6] 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 [4] established that any finitely generated extension always has distinguished subfields. L has the same dimension over any distinguished subfield [5], 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). 
Deveney, James K.; Heerema, Nickolas. Higher Derivations and Distinguished Subfields. Canadian journal of mathematics, Tome 40 (1988) no. 1, pp. 131-141. doi: 10.4153/CJM-1988-006-6
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