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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 subfields of bounded codegree


Authors: James K. Deveney and John N. Mordeson
Journal: Proc. Amer. Math. Soc. 88 (1983), 16-20
MSC: Primary 12F15; Secondary 12F20
MathSciNet review: 691270
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Abstract: Let $ L$ be a function field in $ n > 0$ variables over a field $ K$ of characteristic $ p \ne 0$. An intermediate field $ S$ is maximal separable if $ S$ is separable over $ K$ and every subfield of $ L$ which properly contains $ S$ is inseparable over $ K$. This paper examines when $ [L:S]\vert S$ is maximal separable is bounded. The main result states that this set is bounded if and only if there is an integer $ c$ such that any intermediate field $ {L_1}$ over which $ L$ is purely inseparable and $ [L:{L_1}] > {p^c}$ must be separable over $ K$. Examples are also given where the above bound is $ {p^{n + 1}}$ for any $ n \geqslant 1$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0691270-3
PII: S 0002-9939(1983)0691270-3
Article copyright: © Copyright 1983 American Mathematical Society