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International Conference and Workshop on Valuation Theory
July 26 - August 11, 1999
University of Saskatchewan
Saskatoon, SK, Canada

Organizers
Franz-Viktor Kuhlmann, Salma Kuhlmann, Murray Marshall, Deirdre Haskell, Hans Schoutens

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Generalized Orderings on Fields
by
Tara L. Smith
University of Cincinnati
Coauthors: Louis Mahe (Univ. Rennes), Jan Minac (Univ. Western Ontario)

Let F be a field of characteristic not 2. A certain Galois group over F, the so-called W-group GF of F, carries essentially the same information as the Witt ring WF of F. Given a subgroup H of GF (satisfying certain conditions), we ask when we can find an extension field K of F whose W-group GK is isomorphic to H. This is the Galois-theoretic analogue to finding a field K with Witt ring isomorphic to a certain quotient of WF. It generalizes taking Euclidean closures with respect to a given ordering (or finding a field extension K of F and an isomorphism WK --> Z factoring a given signature WF --> Z). The case of usual orderings corresponds to subgroups isomorphic to Z/2Z.

Date received: June 14, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacv-62.