Counting Generalized Orders on Not Necessarily Formally Real Fields
نویسنده
چکیده
The set of classical orderings of a field compatible with a given place from the field to the real numbers is known to be bijective with the set of homomorphisms from the value group of the place into the two element group. This fact is generalized here to the set of “generalized orders” compatible with an “extended absolute value,” i.e., an absolute value allowed to take the value ∞. The set of extensions to a field F of a given generalized order on a subfield of F is computed and this computation is applied to count the number of such extensions that arise from finite degree field extensions of formally p-adic fields.
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تاریخ انتشار 2004