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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Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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