Fans, real valuations, and hereditarily-Pythagorean fields

William B. Jacob

Vol. 93 (1981), No. 1, 95–105

DOI: 10.2140/pjm.1981.93.95

Abstract

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

Milestones

Received: 2 March 1980

Published: 1 March 1981