<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

Published Online: Aug 24, 2018

Page range: 65 - 78

Received: Apr 01, 2017

Accepted: Nov 08, 2017

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

Keywords
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

Published Online: Aug 24, 2018

Page range: 65 - 78

Received: Apr 01, 2017

Accepted: Nov 08, 2017

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

Keywordsdefect 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.

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