<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

Infinite Towers of Galois Defect Extensions of Kaplansky Fields

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Infinite Towers of Galois Defect Extensions of Kaplansky Fields"}

We give conditions for Kaplansky fields to admit infinite towers of Galois defect extensions of prime degree. As proofs of the presented facts are...

Infinite Towers of Galois Defect Extensions of Kaplansky Fields

Publié en ligne: 24 août 2018

Pages: 65 - 78

Reçu: 01 avr. 2017

Accepté: 08 nov. 2017

DOI: https://doi.org/10.1515/amsil-2017-0012

Mots clés
defect extensions, Kaplansky fields, Artin-Schreier defect extensions, Kummer defect extensions, defectless-by-finite fields

© 2018 Anna Blaszczok, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Infinite Towers of Galois Defect Extensions of Kaplansky Fields

Publié en ligne: 24 août 2018

Pages: 65 - 78

Reçu: 01 avr. 2017

Accepté: 08 nov. 2017

DOI: https://doi.org/10.1515/amsil-2017-0012

Mots clésdefect extensions, Kaplansky fields, Artin-Schreier defect extensions, Kummer defect extensions, defectless-by-finite fields

© 2018 Anna Blaszczok, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
defect extensions, Kaplansky fields, Artin-Schreier defect extensions, Kummer defect extensions, defectless-by-finite fields