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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On subfields of countable codimension
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by A. Białynicki-Birula
Proc. Amer. Math. Soc. 35 (1972), 354-356
DOI: https://doi.org/10.1090/S0002-9939-1972-0304357-4

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.
References
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Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • 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