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Transactions of the American Mathematical Society

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On a Galois theory for inseparable field extensions


Author: John N. Mordeson
Journal: Trans. Amer. Math. Soc. 214 (1975), 337-347
MSC: Primary 12F15
DOI: https://doi.org/10.1090/S0002-9947-1975-0384762-8
MathSciNet review: 0384762
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Abstract: Heerema has developed a Galois theory for fields L of characteristic $ p \ne 0$ in which the Galois subfields K are those for which $ L/K$ is normal, modular and, for some nonnegative integer $ e,K({L^{{p^{e + 1}}}})/K$ is separable. The related automorphism groups G are subgroups of a particular group A of automorphisms on $ L[x]/{x^{{p^e} + 1}}L[x]$ where x is an indeterminate over L. For $ H \subseteq G$ Galois subgroups of A, we give a necessary and sufficient condition for H to be G-invariant. An extension of a result of the classical Galois theory is also given as is a necessary and sufficient condition for every intermediate field of $ L/K$ to be Galois where K is a Galois subfield of L.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0384762-8
Keywords: Higher derivations, normal field extension, modular field extension, purely inseparable field extension, Galois theory
Article copyright: © Copyright 1975 American Mathematical Society

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