Geodesic
The Order of Inseparability of Fields
Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 655-662

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

Let L be a finitely generated field extension of a field K of characteristic p ≠ 0. By Zorn's Lemma there exist maximal separable extensions of K in L and L is finite dimensional purely inseparable over any such field. If ps is the smallest of the dimensions of L over such maximal separable extensions of K in L, then s is Wiel's order of inseparability of L/K [11]. Dieudonné [2] also investigated maximal separable extensions D of K in L and established that there must be at least one D such that L ⊆ Kp–∞(D) (such fields are termed distinguished). Kraft [5] showed that the distinguished maximal separable subfields are precisely those over which L is of minimal degree. This concept of distinguished subfield has been the basis of a number of results on the structure of inseparable field extensions, for example see [1], [3], [5], and [6]. 
Deveney, James K.; Mordeson, John N. The Order of Inseparability of Fields. Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 655-662. doi: 10.4153/CJM-1979-065-3
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