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 | References | Similar Articles | Additional Information
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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Additional Information
Keywords:
Higher derivation,
separable extension,
separably generated,
regular extension,
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Article copyright:
© Copyright 1973
American Mathematical Society