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A NOTE ON DEFECTLESS EXTENSIONS OF HENSELIAN VALUED FIELDS

  • Received : 2021.01.11
  • Accepted : 2021.04.16
  • Published : 2022.01.31
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Abstract

A valued field (K, ν) is called defectless if each of its finite extensions is defectless. In [1], Aghigh and Khanduja posed a question on defectless extensions of henselian valued fields: "if every simple algebraic extension of a henselian valued field (K, ν) is defectless, then is it true that (K, ν) 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, ν) such that each of its simple algebraic extensions is defectless, we investigate additional conditions under which (K, ν) is defectless.

Keywords

Acknowledgement

The author would like to express a deep gratitude to Anna Rzepka (formerly Blaszczok) for her invaluable help. In fact, she presented and proved Theorems 3.3 and 3.6 and made useful comments during the completion of the manuscript.

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