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Transactions of the American Mathematical Society

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

 

 

Higher derivations and field extensions


Author: R. L. Davis
Journal: Trans. Amer. Math. Soc. 180 (1973), 47-52
MSC: Primary 12F15
DOI: https://doi.org/10.1090/S0002-9947-1973-0318115-3
MathSciNet review: 0318115
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Abstract: Let $ K$ be a field having prime characteristic $ p$. The following conditions on a subfield $ k$ of $ K$ are equivalent: (i) $ { \cap _n}{K^{{p^n}}}(k) = k$ and $ K/k$ is separable. (ii) $ k$ is the field of constants of an infinite higher derivation defined in $ K$. (iii) $ k$ is the field of constants of a set of infinite higher derivations defined in $ K$. If $ K/k$ is separably generated and $ k$ is algebraically closed in $ K$, then $ k$ is the field of constants of an infinite higher derivation in $ K$. If $ K/k$ is finitely generated then $ k$ is the field of constants of an infinite higher derivation in $ K$ if and only if $ K/k$ is regular.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0318115-3
Keywords: Higher derivation, separable extension, separably generated, regular extension, $ p$-basis
Article copyright: © Copyright 1973 American Mathematical Society