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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On subfields of countable codimension


Author: A. Białynicki-Birula
Journal: Proc. Amer. Math. Soc. 35 (1972), 354-356
MSC: Primary 12F99
DOI: https://doi.org/10.1090/S0002-9939-1972-0304357-4
MathSciNet review: 0304357
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Abstract: In [2] the authors asked if any two real closed subfields $ R, R'$ of the field of complex numbers C such that $ R(\surd ( - 1)) = R'(\surd ( - 1)) = C$ are isomorphic. It is not difficult to see that the answer is negative. This is proved in the first part of the note. In the second we study the problem if any field which is not prime contains a proper subfield of countable (finite or infinite) codimension.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0304357-4
Article copyright: © Copyright 1972 American Mathematical Society