## Higher derivations and field extensions

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- by R. L. Davis
- Trans. Amer. Math. Soc.
**180**(1973), 47-52 - DOI: https://doi.org/10.1090/S0002-9947-1973-0318115-3
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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.## References

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## Bibliographic Information

- © Copyright 1973 American Mathematical Society
- 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