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Proceedings of the American Mathematical Society

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Normability of certain topological rings

Author: Seth Warner
Journal: Proc. Amer. Math. Soc. 33 (1972), 423-427
MSC: Primary 16A80; Secondary 46H05
MathSciNet review: 0296114
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Abstract: Criteria are given for the nonliability of certain topological rings. These criteria yield generalizations of known theorems on the normability of compact integral domains and topological fields.

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

  • [1] N. Bourbaki, Eléments de mathématique. I: Les structures fondamentales de l'analyse. Fasc. VII, Livre III: Utilisation des nombres réels en topologie générale, 2ième éd., Actualités Sci. Indust., no. 1045, Hermann, Paris, 1958. MR 30 #3439.
  • [2] -, Eléments de mathématique. Fasc. XXVIII. Algèbre commutative. Chaps. 3, 4, Actualités Sci. Indust., no. 1293, Hermann, Paris, 1961. MR 30 #2027.
  • [3] P. M. Cohn, An invariant characterization of pseudo-valuations on a field, Proc. Cambridge Philos. Soc. 50 (1954), 159–177. MR 0064027
  • [4] Irving Kaplansky, Topological rings, Amer. J. Math. 69 (1947), 153–183. MR 0019596
  • [5] Horst Leptin, Linear kompakte Moduln und Ringe, Math. Z. 62 (1955), 241–267 (German). MR 0069811
  • [6] Z. S. Lipkina, Locally bicompact rings without zero divisors, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 1239–1262 (Russian). MR 0219577
  • [7] Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. MR 0120249

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Keywords: Norm, pseudovaluation, topological ring, compact ring
Article copyright: © Copyright 1972 American Mathematical Society