Valuations in real algebra and real algebraic geometry
by
Eberhard Becker
University of Dortmund

A survey is presented how valuations arise in ordered rings and fields and which applications they allow.

Special emphasis is given to the real holomorphy rings of real fields. These rings are a Prüfer rings. This fact and the special structure of their groups of units have many applications to the study of sums of powers in rings and fields. To derive this one needs the socalled Kadison-Dubois representation theorem for Archimedean partially ordered rings. A very strong version of this theorem was recently proved by Jacobi. The role of real valuations and the real holomorphy ring in real algebraic geometry will be sketched.

This talk will concentrate on the field case. In the talk by V. Powers extensions to the case of rings will be discussed.

Date received: July 20, 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-84.