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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Quadratic extensions of linearly compact fields


Authors: Ron Brown and Hoyt D. Warner
Journal: Trans. Amer. Math. Soc. 163 (1972), 379-399
MSC: Primary 12J20; Secondary 13A15
MathSciNet review: 0294307
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Abstract: A group valuation is constructed on the norm factor group of a quadratic extension of a linearly compact field, and the norm factor group is explicitly computed as a valued group. Generalizations and applications of this structure theory are made to cyclic extensions of prime degree, to square (and $ p$th power) factor groups, to generalized quaternion algebras, and to quadratic extensions of arbitrary fields.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0294307-6
PII: S 0002-9947(1972)0294307-6
Keywords: Linearly compact field, maximal field, valuation, quadratic field extension, norm factor group, square factor group, ramification, generalized quaternion algebra, quadratic forms, valued group, filtered group, ultracomplete valued group, graded group, well ordered product, Hahn product, Henselian field
Article copyright: © Copyright 1972 American Mathematical Society