On rank of extensions of valuations
Subfields of henselian valued fields
Let (K,v) be a henselian valued field of arbitrary rank which is not separably closed. Let k be a subfield of K of finite codimension and be the valuation obtained by restricting v to k. We give some necessary and sufficient conditions for to be henselian. In particular, it is shown that if k is dense in its henselization, then is henselian. We deduce some well known results proved in this direction through other considerations.
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