Monogenity of iterates of polynomials
Article Type
Research Article
Publication Title
Archiv Der Mathematik
Abstract
In this article, we study the monogenity of a tower of number fields defined by the iterates of a stable polynomial. We give a necessary condition for the monogenity of the number fields defined by the iterates of a stable polynomial. When the stable polynomial is of certain type, we also give a sufficient condition for the monogenity of the fields defined by each of its iterate. As a consequence, we obtain an infinite 3-tower of monogenic number fields. Moreover, we construct an infinite family of stable polynomials such that each of its iterate is non-monogenic.
First Page
295
Last Page
305
DOI
10.1007/s00013-023-01949-9
Publication Date
3-1-2024
Recommended Citation
Sharma, Himanshu; Sarma, Ritumoni; and Laishram, Shanta, "Monogenity of iterates of polynomials" (2024). Journal Articles. 4910.
https://digitalcommons.isical.ac.in/journal-articles/4910