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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Distinguished subfields


Authors: James K. Deveney and John N. Mordeson
Journal: Trans. Amer. Math. Soc. 260 (1980), 185-193
MSC: Primary 12F15
MathSciNet review: 570785
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Abstract: Let L be a finitely generated nonalgebraic extension of a field K of characteristic $ p\, \ne \,0$. A maximal separable extension D of K in L is distinguished if $ L\, \subseteq \,{K^{{p^{ - \,n}}}}(D)$ for some n. Let d be the transcendence degree of L over K. If every maximal separable extension of K in L is distinguished, then every set of d relatively p-independent elements is a separating transcendence basis for a distinguished subfield. Conversely, if $ K({L^p})$ is separable over K, this condition is also sufficient. A number of properties of such fields are determined and examples are presented illustrating the results.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0570785-4
PII: S 0002-9947(1980)0570785-4
Keywords: Distinguished subfields, modular field extension, irreducible field extension
Article copyright: © Copyright 1980 American Mathematical Society