On Indices of Septic Number Fields Defined by Trinomials x 7 + ax + b

Lhoussain El Fadil ()
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Lhoussain El Fadil: Department of Mathematics, Faculty of Sciences Dhar El Mahraz-Fes, Sidi Mohamed Ben Abdellah University, Fez P.O. Box 1796, Morocco

Mathematics, 2023, vol. 11, issue 21, 1-12

Abstract: Let K be a septic number field generated by a root, α , of an irreducible trinomial, x 7 + a x + b ∈ Z [ x ] . In this paper, for every prime integer, p , we calculate ν p ( i ( K ) ) ; the highest power of p dividing the index, i ( K ) , of the number field, K . In particular, we calculate the index, i ( K ) . In 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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