Finite Codimension Subfields of a Field Complete with Respect to a Real Valuation

Bevelacqua, Anthony J.; Motley, Mark

doi:10.1080/00927870500346313

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2010

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Cited by 2 publications

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“…In 2006, Bevelacqua and Motley [1] characterized those complete rank one valued fields (K, v) whose each subfield of finite codimension is complete. They proved that if K is not an algebraically closed field, then every finite codimensional subfield of K is complete in the v-adic topology if and only if either the characteristic of K is zero or the characteristic is p > 0 and [K :…”

Section: Introductionmentioning

confidence: 99%

Subfields of henselian valued fields

Khassa

Khanduja

2010

Colloq. Math.

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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. In this paper, 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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Section: Introductionmentioning

confidence: 99%