Research Article

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

Published in: Quaestiones Mathematicae
Volume 49 , issue 2 , 2026 , 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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