Infinite towers of Galois defect extensions of Kaplansky fields

Anna Blaszczok

Published: 2018-01-31

Vol. 32 (2018)

Infinite towers of Galois defect extensions of Kaplansky fields

Anna Blaszczok

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

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References

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Vol. 32 (2018)
Published: 2018-08-24

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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