Communications of the
Korean Mathematical Society CKMS

A valued field $(K,v)$ is called defectless if each of its finite extensions is defectless. In cite{a.k.o.2002}, Aghigh and Khanduja posed a question on defectless extensions of henselian valued fields: ``if every simple algebraic extension of a henselian valued field $(K,v)$ is defectless, then is it true that $(K,v)$ is defectless?'' They gave an example to show that the answer is ``no'' in general. This paper explores when the answer to the mentioned question is affirmative. More precisely, for a henselian valued field $(K,v)$ such that each of its simple algebraic extensions is defectless, we investigate additional conditions under which $(K,v)$ is defectless.

Keywords: Valued fields, non-Archimedean valued fields, valuations and their generalizations for commutative rings

MSC numbers: Primary 12J10, 12J25, 13A18