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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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Keywords: Higher derivation, separable extension, separably generated, regular extension, <IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$p$">-basis
Article copyright: © Copyright 1973 American Mathematical Society