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

 

On Galois theory using pencils of higher derivations


Authors: James K. Deveney and John N. Mordeson
Journal: Proc. Amer. Math. Soc. 72 (1978), 233-238
MSC: Primary 12F15
MathSciNet review: 507314
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Abstract: Let $ L \supset K$ be fields of characteristic $ p \ne 0$. Assume K is the field of constants of a group of pencils of higher derivations on L, and hence L is modular over K and K is separably algebraically closed in L. Every intermediate field F which is separably algebraically closed in L and over which L is modular is the field of constants of a group of pencils of higher derivations if and only if $ K({L^{{p^e}}})$ has a finite separating transcendence basis over K for some nonnegative integer e. If $ p \ne 2,3$ and $ K({L^{{p^e}}})$ does have a finite separating transcendence basis over K, and F is the field of constants of a group of pencils, then the group of L over F is invariant in the group of L over K if and only if $ F = K({L^{{p^r}}})$ for some nonnegative integer r.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0507314-3
PII: S 0002-9939(1978)0507314-3
Keywords: Modular field extension, pencils of higher derivations
Article copyright: © Copyright 1978 American Mathematical Society