Infinite towers of Galois defect extensions of Kaplansky fields



Abstract

We give conditions for Kaplansky fields to admit infinite towers of Galois defect extensions of prime degree. As proofs of the presented facts are constructive, this provides examples of constructions of infinite towers of Galois defect extensions of prime degree. We also give a constructive proof of the fact that a henselian Kaplansky field cannot be defectless-by-finite.


Keywords

defect extensions; Kaplansky fields; Artin–Schreier defect extensions; Kummer defect extensions; defectless-by-finite fields

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Published : 2018-01-31


BlaszczokA. (2018). Infinite towers of Galois defect extensions of Kaplansky fields. Annales Mathematicae Silesianae, 32, 65-78. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/13913

Anna Blaszczok  anna.blaszczok@us.edu.pl
Instytut Matematyki, Uniwersytet Śląski w Katowicach  Poland



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