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 | References | Similar Articles | Additional Information
Abstract: Heerema has developed a Galois theory for fields L of characteristic in which the Galois subfields K are those for which
is normal, modular and, for some nonnegative integer
is separable. The related automorphism groups G are subgroups of a particular group A of automorphisms on
where x is an indeterminate over L. For
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
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