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On Index Divisors and Monogenity of Certain Number Fields Defined by Trinomials x7+ax+b
Version 1
: Received: 5 September 2023 / Approved: 7 September 2023 / Online: 7 September 2023 (07:08:03 CEST)
A peer-reviewed article of this Preprint also exists.
El Fadil, L. On Indices of Septic Number Fields Defined by Trinomials x7 + ax + b. Mathematics 2023, 11, 4441. El Fadil, L. On Indices of Septic Number Fields Defined by Trinomials x7 + ax + b. Mathematics 2023, 11, 4441.
Abstract
In this paper for every number field K generated by a root α of a trinomial x7 + ax + b ∈ Z[x] and for every prime integer p, we calculate νp(i(K)), the highest power of p dividing the index i(K) of the field K. In particular, we calculate the index i(K). As application, when the index of K is not trivial, then K is not monogenic.
Keywords
Power integral bases; theorem of Ore; prime ideal factorization; common index divisor
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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