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Proceedings of the American Mathematical Society

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

 
 

 

Fields with few extensions


Authors: J. Knopfmacher and A. M. Sinclair
Journal: Proc. Amer. Math. Soc. 29 (1971), 255-258
MSC: Primary 12.70
DOI: https://doi.org/10.1090/S0002-9939-1971-0274426-5
MathSciNet review: 0274426
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Abstract: We show that a valued field $ \Lambda $ with only a finite number of nonisomorphic valued extensions is equal to the complex field C or is real closed with $ C = \Lambda (\surd ( - 1))$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0274426-5
Keywords: Valuations, real closed fields, algebraically closed fields, real field, complex field
Article copyright: © Copyright 1971 American Mathematical Society

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