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A note on monogenity of certain pure number fields defined by $x^{p^r}{-}a$ with non-square-free parameter

Omar Kchit
Vol. 12 (2023), No. 2, 147–164
DOI: 10.2140/moscow.2023.12.147
Abstract

Let K = ℚ(α) be a pure number field generated by a root α of a monic irreducible polynomial F(x) = xpr − a ∈ ℤ[x], where p is a rational prime and r is a positive integer. We study the monogenity of K. We illustrate our results by some computational examples.

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Keywords
Dedekind's theorem, Ore's theorem, prime ideal factorization, Newton polygon, index of a number field, monogenic
Mathematical Subject Classification
Primary: 11R04, 11Y40, 11R21
Milestones
Received: 22 January 2023
Revised: 17 February 2023
Accepted: 4 March 2023
Published: 4 June 2023
Authors
Omar Kchit
Faculty of Sciences Dhar El Mahraz
Sidi Mohamed ben Abdellah University
Fes
Morocco
© 2023 MSP (Mathematical Sciences Publishers).