Geodesic
On Purely Inseparable Extensions of Unbounded Exponent
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1526-1532

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

Let L/K be a field extension of characteristic p ≠ 0. If L/K is purely inseparable and of bounded exponent, then the property that L has a subbasis over K (11, p. 436) is of significance in the theory of higher derivations (11) and in the theory of Hopf algebras (9; 10). In this case, where L/K is of bounded exponent, it has been shown independently in (1; 9; 5) that L/K having a sub-basis is equivalent to the property that L/K is modular (9, p. 401). Our aim in this paper is to extend and apply these properties for L/K purely inseparable and of unbounded exponent.In Theorem 1, we give several conditions on a p-basis of L which are equivalent to the property that L/K has a sub-basis. In Theorem 2, we give a sequence of implications starting with L/K has a sub-basis. 
Haddix, G. F.; Mordeson, J. N.; Vinograde, B. On Purely Inseparable Extensions of Unbounded Exponent. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1526-1532. doi: 10.4153/CJM-1969-167-1
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