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Note on a variation of the Schröder-Bernstein problem for fields. (English) Zbl 1011.12002

Summary: In this note we study fields \(F\) with the property that the simple transcendental extension \(F(u)\) of \(F\) is isomorphic to some subfield of \(F\) but not isomorphic to \(F\). Such a field provides one type of solution of the Schröder-Bernstein problem for fields.

MSC:

12F05 Algebraic field extensions
12F20 Transcendental field extensions
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References:

[1] W. T. Gowers: A solution to the Schröder-Bernstein problem for Banach spaces. Bull. London Math. Soc. 28 (1996), 297-304. · Zbl 0863.46006 · doi:10.1112/blms/28.3.297
[2] I. Kaplansky: Infinite Abelian Groups. Revised edition, University of Michigan Press, 1969. · Zbl 0194.04402
[3] J. Kelley: General Topology. D. van Nostrand, New York, 1955. · Zbl 0066.16604
[4] B. L. van der Waerden: Modern Algebra. Vol. 1. Ungar, New York, 1953.
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