# Valuation rings residue and quotient fields

*From*: Jose Capco <jcapco@xxxxxxxxx>*Date*: Sun, 01 Mar 2009 17:14:40 EST

Dear NG,

Is there an example (preferably easy) of a valuation ring by which its Krull dimension is 1 and that its residue field has two orderings (say something like Q(sqrt(2))) and its quotient field has only one ordering (say something like R)?

Sincerely,

Jose Capco

.

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