Vol. 30, No. 2, 1969

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An embedding theorem for lattice-ordered fields

Paul F. Conrad and John Dauns

Vol. 30 (1969), No. 2, 385–398

In this paper we develop a method for constructing latticeordered fields (“-fields”) which are not totally ordered (“o-fields”) and hence are not f-rings. We show that many of these fields admit a Hahn type embedding into a field of formal power series with real coefficients. In order to establish such an embedding we make use of the valuation theory for abelian -groups and prove the “well known” fact that each o-field can be embedded in an o-field of formal power series.

Mathematical Subject Classification
Primary: 12.70
Secondary: 06.00
Received: 15 April 1968
Published: 1 August 1969
Paul F. Conrad
John Dauns