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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

An intermediate theory for a purely inseparable Galois theory


Author: James K. Deveney
Journal: Trans. Amer. Math. Soc. 198 (1974), 287-295
MSC: Primary 12F15
DOI: https://doi.org/10.1090/S0002-9947-1974-0417141-4
MathSciNet review: 0417141
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Abstract: Let $ K$ be a finite dimensional purely inseparable modular extension of $ F$, and let $ L$ be an intermediate field. This paper is concerned with an intermediate theory for the Galois theory of purely inseparable extensions using higher derivations [4]. If $ L$ is a Galois intermediate field and $ M$ is the field of constants of all higher derivations on $ L$ over $ F$, we prove that every higher derivation on $ L$ over $ F$ extends to $ K$ if and only if $ K = L{ \otimes _M}J$ for some field $ J$. Similar to classical Galois theory the distinguished intermediate fields are those which are left invariant under a standard generating set for the group of all rank $ t$ higher derivations on $ K$ over $ F$. We prove: $ L$ is distinguished if and only if $ L$ is $ M$-homogeneous (4.9).


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DOI: https://doi.org/10.1090/S0002-9947-1974-0417141-4
Keywords: Higher derivation, iterative higher derivation, dual basis, $ M$-homogeneous intermediate fields
Article copyright: © Copyright 1974 American Mathematical Society