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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Maximal separable intermediate fields of large codegree


Author: Nickolas Heerema
Journal: Proc. Amer. Math. Soc. 82 (1981), 351-354
MSC: Primary 12F15; Secondary 12F20
MathSciNet review: 612717
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Abstract: Let $ k$ be a function field in $ n(n > 0)$ variables over $ {k_0}$ a field having characteristic $ p \ne 0$. An intermediate field $ s$ is maximal separable if $ s/{k_0}$ is separable and $ s$ is not properly contained in any subfield of $ k$ separable over $ {k_0}$. The following result is proved. If $ n = 1$ the set $ \Delta = \{ [k:s]\vert s$ maximal separable} is bounded if and only if the algebraic closure $ {\bar k_0}$ of $ {k_0}$ in $ k$ is separable over $ {k_0}$. If $ n \geqslant 1$ and $ \Delta $ is bounded then $ {\bar k_0}/{k_0}$ is separable. An upper bound for $ \Delta $ is obtained for the case $ n = 1$ and $ {\bar k_0}/{k_0}$ separable.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0612717-2
PII: S 0002-9939(1981)0612717-2
Article copyright: © Copyright 1981 American Mathematical Society