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Proceedings of the American Mathematical Society

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

 

 

Determination of quadratic extensions of linearly compact fields by norm groups


Author: Hoyt D. Warner
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0294308-3
Keywords: Quadratic extensions, linearly compact fields, norm groups, group valuation
Article copyright: © Copyright 1972 American Mathematical Society