New York Journal of Mathematics
Volume 28 (2022), 650-658


Anuj Jakhar

Nonmonogenity of number fields defined by trinomials

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Published: March 27, 2022.
Keywords: Monogenity, non-monogenity, Newton polygon, power basis.
Subject: 11R04.

Let f(x) = xn-axm-b be a monic irreducible polynomial of degree n having integer coefficients. Let K = Q(θ) be an algebraic number field with θ a root of f(x). In this paper, we provide some explicit conditions involving only a, b, m, n for which K is not monogenic. Further, as an application, in a special case, we show that if p is a prime number of the form 32k+1, k ∈ Z and θ is a root of a monic polynomial x32n-64axm-p with n odd and a divisible by p, then Q(θ) is not monogenic.


The author is supported by the SERB Start-up Research Grant SRG/2021/000393.

Author information

Anuj Jakhar:
Department of Mathematics
Indian Institute of Technology (IIT) Bhilai
Chhattisgarh 492015, India