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Title: Note on a variation of the Schröder-Bernstein problem for fields (English)
Author: Cater, F. S.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 52
Issue: 4
Year: 2002
Pages: 717-720
Summary lang: English
Category: math
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. (English)
Keyword: field
Keyword: subfield
Keyword: isomorphism
Keyword: transcendental extension
Keyword: algebraic extension
MSC: 12E99
MSC: 12F05
MSC: 12F20
idZBL: Zbl 1011.12002
idMR: MR1940052
Date available: 2009-09-24T10:55:49Z
Last updated: 2020-07-03
Stable URL:
Reference: [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, MR 1374409, 10.1112/blms/28.3.297
Reference: [2] I. Kaplansky: Infinite Abelian Groups.Revised edition, University of Michigan Press, 1969. Zbl 0194.04402, MR 0233887
Reference: [3] J. Kelley: General Topology.D. van Nostrand, New York, 1955. Zbl 0066.16604, MR 0070144
Reference: [4] B. L. van der Waerden: Modern Algebra. Vol. 1.Ungar, New York, 1953.


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