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Subfields of henselian valued fields

Ramneek Khassa, Sudesh K. Khanduja (2010)

Colloquium Mathematicae

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 v k be the valuation obtained by restricting v to k. We give some necessary and sufficient conditions for ( k , v k ) to be henselian. In particular, it is shown that if k is dense in its henselization, then ( k , v k ) is henselian. We deduce some well known results proved in this direction through other considerations.

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