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.


12F05 Algebraic field extensions
12F20 Transcendental field extensions
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