Vol. 93, No. 1, 1981

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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