Vol. 93, No. 1, 1981

Recent Issues
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
Fans, real valuations, and hereditarily-Pythagorean fields

William B. Jacob

Vol. 93 (1981), No. 1, 95–105

In this paper we give an explicit description of valuation rings compatible with certain infinite preprimes of a field. These results are essentially constructive versions of the results of L. Brocker and E. Becker relating fans and valuations. We discuss a number of examples in detail, including the higher orderings recently introduced by E. Becker. One of several applications is a generalization of the theorem of Brocker-Brown characterizing superpythagorean fields.

Mathematical Subject Classification 2000
Primary: 12D15
Secondary: 10C05
Received: 2 March 1980
Published: 1 March 1981
William B. Jacob
University of California, Santa Barbara
Santa Barbara CA
United States