Dutta A.2025-02-1720230http://dx.doi.org/10.1002/mana.202200178https://idr.iitbbs.ac.in/handle/2008/4589Given a valued field (Figure presented.) and its completion (Figure presented.), we study the set of all possible extensions of v to (Figure presented.). We show that any such extension is closely connected with the underlying subextension (Figure presented.). The connections between these extensions are studied via minimal pairs, key polynomials, pseudo-Cauchy sequences, and implicit constant fields. As a consequence, we obtain strong ramification theoretic properties of (Figure presented.). We also give necessary and sufficient conditions for (Figure presented.) to be dense in (Figure presented.). � 2023 Wiley-VCH GmbH.encompletion of valuations; extension of valuation to rational function fields; implicit constant fields; key polynomials; minimal pairs; pseudo Cauchy sequences; valuationArticle