Research Article

An infinite family of number fields arising from quadrinomials with given p-indices

Published in: Quaestiones Mathematicae
Volume 49 , issue 2 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 183–194

DOI: 10.2989/16073606.2025.2568831

Author(s): Omar Kchit Sidi Mohamed ben Abdellah University, Morocco,

Keywords: 11R04, 11Y40, 11R21, Theorem of Dedekind, theorem of Ore, prime ideal factorization, Newton polygon, index of a number field, monogenic,

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Abstract

Let be a number field defined by a monic irreducible quadrinomial , where n > m > 1 are positive integers. In this paper, for any prime number p and for some fixed positive integers i_p , we provide infinite families of number fields defined by this family of quadrinomials satisfying ν_p (i(K )) = i_p . As an application of our results, if i(K ) ≠ 1, then K is not monogenic. We illustrate our results by some computational examples.

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Research Article

An infinite family of number fields arising from quadrinomials with given p-indices

Abstract

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