Geodesic
Distinguished Subfields of Intermediate Fields
Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1085-1096

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

Let L be a finitely generated extension of a field K of characteristic p ≠ 0. If L/K is algebraic, then there is a unique intermediate field S such that S is just the maximal separable extension of K in L. If L/K is not algebraic, then Dieudonne [4] showed there exist maximal separable extensions D of K in L such that L ⊆ Kp–∞⊗KD. In general, not every maximal separable extension of K in L has the property. Those which do have the property are called distinguished. Kraft [7] established that a maximal separable extension D of K in L is distinguished if and only if [L:D] is as small as possible. If the minimum of the [L:D] is pr , r is called the order of inseparability of L/K, denoted inor (L/K).Let L 1 be an intermediate field of L/K. If L/K is algebraic, then the maximal separable extension S 1 of K in L 1 is contained in the maximal separable extension S of K in L, and moreover S is separable over S 1. 
Deveney, James K.; Mordeson, John N. Distinguished Subfields of Intermediate Fields. Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1085-1096. doi: 10.4153/CJM-1981-083-2
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