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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Fields of constants of infinite higher derivations

Author: James K. Deveney
Journal: Proc. Amer. Math. Soc. 41 (1973), 394-398
MSC: Primary 12F10; Secondary 12F15
MathSciNet review: 0335478
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Abstract: Let $ K$ be a field of characteristic $ p \ne 0$, and let $ P$ be its maximal perfect subfield. Let $ h$ be a subfield of $ K$ containing $ P$ such that $ K$ is separable over $ h$. We prove: Every regular subfield of $ K$ containing $ h$ is the field of constants of a set of higher derivations on $ K$ if and only if (1) the transcendence degree of $ K$ over $ h$ is finite, and (2) $ K$ has a separating transcendency basis over $ h$. This result leads to a generalization of the Galois theory developed in [4].

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Keywords: Higher derivation, regular extension field
Article copyright: © Copyright 1973 American Mathematical Society

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