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Decomposition of Witt Rings and Galois Groups

Published online by Cambridge University Press:  20 November 2018

Ján Mináč  and
Tara L. Smith
Ján Mináč
Affiliation:
Department of Mathematics University of Western Ontario London, Ontario N6A 5B7
Tara L. Smith
Affiliation:
Department of Mathematical Sciences University of Cincinnati Cincinnati, Ohio 45221-0025 U.S.A.
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Abstract

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To each field F of characteristic not 2, one can associate a certain Galois group 𝒢F, the so-called W-group of F, which carries essentially the same information as the Witt ring W(F) of F. In this paper we show that direct products of Witt rings correspond to free products of these Galois groups (in the appropriate category), group ring construction of Witt rings corresponds to semidirect products of W-groups, and the basic part of W(F) is related to the center of 𝒢F. In an appendix we provide a complete list of Witt rings and corresponding w-groups for fields F with |Ḟ/Ḟ2| ≤ 16.

Keywords

11E81
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 6 , 01 December 1995 , pp. 1274 - 1289
Copyright
Copyright © Canadian Mathematical Society 1995

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