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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Pencils of higher derivations of arbitrary field extensions


Authors: James K. Deveney and John N. Mordeson
Journal: Proc. Amer. Math. Soc. 74 (1979), 205-211
MSC: Primary 12F15
MathSciNet review: 524286
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Abstract: Let L be a field of characteristic $ p \ne 0$. A subfield K of L is Galois if K is the field of constants of a group of pencils of higher derivations on L. Let $ F \supset K$ be Galois subfields of L. Then the group of L over F is a normal subgroup of the group of L over K if and only if $ F = K({L^{{p^r}}})$ for some nonnegative integer r. If $ L/K$ splits as the tensor product of a purely inseparable extension and a separable extension, then the algebraic closure of K in L, $ \bar K$, is also Galois in L. Given K, for every Galois extension L of K, $ \bar K$ is also Galois in L if and only if $ [K:{K^p}] < \infty $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0524286-7
PII: S 0002-9939(1979)0524286-7
Keywords: Modular field extension, pencils of higher derivations
Article copyright: © Copyright 1979 American Mathematical Society