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Maximal subfields of algebraically closed fields

Part of: Field extensions

Published online by Cambridge University Press:  09 April 2009

Robert M. Guralnick  and
Michael D. Miller
Robert M. Guralnick
Affiliation:
Department of Mathematics University of CaliforniaLos Angeles, California, U.S.A.
Michael D. Miller
Affiliation:
Department of Mathematics University of CaliforniaLos Angeles, California, U.S.A.
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Abstract

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Let K be an algebraically closed field of characteristic zero, and S a nonempty subset of K such that S Q = Ø and card S < card K, where Q is the field of rational numbers. By Zorn's Lemma, there exist subfields F of K which are maximal with respect to the property of being disjoint from S. This paper examines such subfields and investigates the Galois group Gal K/F along with the lattice of intermediate subfields.

MSC classification

Secondary: 12F05: Algebraic extensions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 4 , June 1980 , pp. 462 - 468
Copyright
Copyright © Australian Mathematical Society 1980

References

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