<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this work we generalize the results of [9] to the higher level case: we define <italic>n</italic>-th root selections in fields of characteristic ≠ 2, that is subgroups of the multiplicative group of a field whose existence is equivalent to the existence of a partial inverse of the <italic>x</italic> ↦ <italic>x<sup>n</sup></italic> function, provide necessary and sufficient conditions for such a subgroup to exist, study their existence under field extensions, and give some structural results describing the behaviour of maximal n-th root selection fields.</p></abstract>

In this work we generalize the results of [9] to the higher level case: we define n-th root selections in fields of characteristic ≠ 2, that is subgroups of the multiplicative group of a field whose existence is equivalent to the existence of a partial inverse of the x ↦ xn function, provide necessary and sufficient conditions for such a subgroup to exist, study their existence under field extensions, and give some structural results describing the behaviour of maximal n-th root selection fields.

<italic>n</italic>-TH Root Selections in Fields

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":{"italic":"n","content":"-TH Root Selections in Fields"}}

In this work we generalize the results of [9] to the higher level case: we define n-th root selections in fields of characteristic ≠ 2, that is subgroups of...

n-TH Root Selections in Fields

Published Online: Jul 18, 2019

Page range: 106 - 120

Received: Apr 05, 2018

Accepted: Jun 01, 2019

DOI: https://doi.org/10.2478/amsil-2019-0012

Keywords
root selections, root selections of higher level, half-orderings, pre-orderings and orderings of higher level

© 2019 Paweł Gładki, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

n-TH Root Selections in Fields

Published Online: Jul 18, 2019

Page range: 106 - 120

Received: Apr 05, 2018

Accepted: Jun 01, 2019

DOI: https://doi.org/10.2478/amsil-2019-0012

Keywordsroot selections, root selections of higher level, half-orderings, pre-orderings and orderings of higher level

© 2019 Paweł Gładki, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
root selections, root selections of higher level, half-orderings, pre-orderings and orderings of higher level