A note on defectless extensions of henselian valued fields
Commun. Korean Math. Soc. Published online July 8, 2021
Ayatollah Boroujerdi University
Abstract : Let v be a henselian valuation on a field K and ¯ v be the
unique extension of v to a fixed algebraic closure K ̅ of K. The valued
field (K, v) is defectless if each finite extension of (K, v) is defectless. In
, Aghigh and Khanduja posed a question on defectless extensions, " If
K(θ)/K is defectless for each θ ∈( K) ̅\K, then is it true that (K, v) is
defectless?" They gave an example to show that the answer is "no" in
general. In this paper, it is investigated the conditions under which the
answer to the mentioned question is affirmative.
Keywords : Valued fields, non-Archimedean valued fields, valuations and their generalizations for commutative rings.