A note on defectless extensions of henselian valued fields
Commun. Korean Math. Soc. 2022 Vol. 37, No. 1, 65-74
Published online July 8, 2021
Printed January 31, 2022
Azadeh Nikseresht
Ayatollah Boroujerdi University
Abstract : 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
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