Determination of quadratic extensions of linearly compact fields by norm groups
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- by Hoyt D. Warner PDF
- Proc. Amer. Math. Soc. 34 (1972), 1-7 Request permission
Abstract:
It is shown that quadratic extensions of a field not of characteristic two, which is linearly compact at a valuation, are determined by their groups of norms, provided the residue field has a unique quadratic extension and is perfect if of characteristic two. It is indicated that Henselian can replace linearly compact in some cases. Necessity of the condition on the residue field is shown.References
- 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
- Ron Brown and Hoyt D. Warner, Quadratic extensions of linearly compact fields, Trans. Amer. Math. Soc. 163 (1972), 379–399. MR 294307, DOI 10.1090/S0002-9947-1972-0294307-6
- O. F. G. Schilling, The Theory of Valuations, Mathematical Surveys, No. 4, American Mathematical Society, New York, N. Y., 1950. MR 0043776
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 1-7
- MSC: Primary 12J10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0294308-3
- MathSciNet review: 0294308