*-valuations and hermitian forms on skew fields
by
Tom Craven
University of Hawaii

We work with a skew field (division ring) D with an involution *. In this case one has the classical theory of hermitian forms and a Witt group of equivalence classes of anisotropic forms. When D is commutative, the Witt ring determines the set of total orderings of D, and the (Krull) valuations compatible with these orderings are very important to the structure of the Witt ring. We will survey the proposed generalizations of the concept of ordering to the pair (D,*), along with how they relate to valuation theory and the Witt group. An old survey paper (conference in 1992) on this topic is available at:

http://www.math.hawaii.edu/~tom/papers.html

Date received: May 21, 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-52.