|
|||||
|
|
|
|
|
|
|
|
|
An embedding theorem
for lattice-ordered fields
Paul F. Conrad and John Dauns |
|
Vol. 30 (1969), No. 2, 385–398
|
Abstract |
|
In this paper we develop a method for constructing latticeordered fields (“ℒ-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 ℒ-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
|
Milestones
Received: 15 April 1968
Published: 1 August 1969
|
Authors |
| Paul F. Conrad | |
| John Dauns | |
|
