Fields with few extensions
HTML articles powered by AMS MathViewer
- by J. Knopfmacher and A. M. Sinclair PDF
- Proc. Amer. Math. Soc. 29 (1971), 255-258 Request permission
Abstract:
We show that a valued field $\Lambda$ with only a finite number of nonisomorphic valued extensions is equal to the complex field $\mathbfit {C}$ or is real closed with $C = \Lambda (\surd ( - 1))$.References
-
R. Baer and H. Hasse, Zusammenhung und Dimension topologischer Körperräume, J. Reine Angew. Math. 167 (1932), 40-45.
- N. Bourbaki, Éléments de mathématique. Fasc. XXX. Algèbre commutative. Chapitre 5: Entiers. Chapitre 6: Valuations, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1308, Hermann, Paris, 1964 (French). MR 0194450
- Ervin Fried, Algebraically closed fields as finite extensions, Mat. Lapok 7 (1956), 47–60 (Hungarian, with English and Russian summaries). MR 99977
- Nathan Jacobson, Lectures in abstract algebra. Vol III: Theory of fields and Galois theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London-New York, 1964. MR 0172871
- Serge Lang, Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR 0197234
- Lawrence Narici, On nonarchimedian Banach algebras, Arch. Math. (Basel) 19 (1968), 428–435. MR 236711, DOI 10.1007/BF01898426
- Niel Shilkret, Non-Archimedean Gelfand theory, Pacific J. Math. 32 (1970), 541–550. MR 257752
Additional Information
- © Copyright 1971 American Mathematical Society
- 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