 

Anuj Jakhar
Nonmonogenity of number fields defined by trinomials
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Published: 
March 27, 2022. 
Keywords: 
Monogenity, nonmonogenity, Newton polygon, power basis. 
Subject: 
11R04. 


Abstract
Let f(x) = x^{n}ax^{m}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
x^{32n}64ax^{m}p with n odd and a divisible by p, then Q(θ) is not monogenic.


Acknowledgements
The author is supported by the SERB Startup Research Grant SRG/2021/000393.


Author information
Anuj Jakhar:
Department of Mathematics
Indian Institute of Technology (IIT) Bhilai
Chhattisgarh 492015, India
anujjakhar@iitbhilai.ac.in

