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

Let <italic>K</italic> be a pure number field generated by a root <italic>α</italic> of a monic irreducible polynomial <italic>f</italic> (<italic>x</italic>)= <italic>xn</italic> − <italic>m</italic> with <italic>m</italic> a rational integer and 3 <italic>≤</italic> <italic>n</italic> ≤ 9 an integer. In this paper, we calculate an integral basis of ℤ<italic>K</italic> , and we study the monogenity of <italic>K</italic>, extending former results to the case when <italic>m</italic> is not necessarily square-free. Collecting and completing the corresponding results in this more general case, our purpose is to provide a parallel to [Gaál, I.—Remete, L.: <italic>Power integral bases and monogenity of pure fields</italic>,J.Number Theory, <bold>173</bold> (2017), 129–146], where only square-free values of <italic>m</italic> were considered.
</abstract>

Let K be a pure number field generated by a root α of a monic irreducible polynomial f (x)= xn − m with m a rational integer and 3  ≤ n ≤ 9 an integer. In this paper, we calculate an integral basis of ℤK , and we study the monogenity of K, extending former results to the case when m is not necessarily square-free. Collecting and completing the corresponding results in this more general case, our purpose is to provide a parallel to [Gaál, I.—Remete, L.: Power integral bases and monogenity of pure fields,J.Number Theory, 173 (2017), 129–146], where only square-free values of m were considered.

Integral Bases and Monogenity of Pure Number Fields with Non-Square Free Parameters up to Degree 9

Tatra Mountains Mathematical Publications

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

Let K be a pure number field generated by a root α of a monic irreducible polynomial f (x)= xn − m with m a rational integer and 3  ≤ n ≤ 9 an integer. In this...

Integral Bases and Monogenity of Pure Number Fields with Non-Square Free Parameters up to Degree 9

Published Online: Mar 07, 2023

Page range: 61 - 86

Received: Nov 10, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0006

Keywords
integral bases, power integral basis, index, theorem of Ore, Newton polygon

© 2023 Mathematical Institute, Slovak Academy of Sciences

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

Integral Bases and Monogenity of Pure Number Fields with Non-Square Free Parameters up to Degree 9

Published Online: Mar 07, 2023

Page range: 61 - 86

Received: Nov 10, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0006

Keywordsintegral bases, power integral basis, index, theorem of Ore, Newton polygon

© 2023 Mathematical Institute, Slovak Academy of Sciences

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

Keywords
integral bases, power integral basis, index, theorem of Ore, Newton polygon