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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Higher derivation Galois theory of fields


Author: Nickolas Heerema
Journal: Trans. Amer. Math. Soc. 265 (1981), 169-179
MSC: Primary 12F15
MathSciNet review: 607115
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Abstract: A Galois correspondence for finitely generated field extensions $ k/h$ is presented in the case characteristic $ h = p \ne 0$. A field extension $ k/h$ is Galois if it is modular and $ h$ is separably algebraically closed in $ k$. Galois groups are the direct limit of groups of higher derivations having rank a power of $ p$. Galois groups are characterized in terms of abelian iterative generating sets in a manner which reflects the similarity between the finite rank and infinite rank theories of Heerema and Deveney [9] and gives rise to a theory which encompasses both. Certain intermediate field theorems obtained by Deveney in the finite rank case are extended to the general theory.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0607115-6
PII: S 0002-9947(1981)0607115-6
Article copyright: © Copyright 1981 American Mathematical Society