Real holomorphy rings and sums of 2n-th powers in fields and rings
by
Victoria Powers
Emory University

The real holomorphy ring of a real field K is the intersection of all real valuations rings in K. It is used extensively in the study of quadratic forms, orders, higher level orders and sums of 2n-th powers, and in real algebraic geometry. The definite of the real holomorphy ring and many of the results for fields can be extended to arbitrary commutative rings. In this talk we will survey the theory of the real holomorphy ring and discuss its use in the study of higher level orders and sums of 2n-th powers in fields and commutative rings.

Date received: February 8, 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-06.