A note on non-monogenity of number fields arised from sextic trinomials

Abstract

Let K = Q (θ) be an algebraic number field with θ a root of an irreducible polynomial f(x) = x ⁶ + ax^m + b belonging to ℤ[x] and 1 ≤ m ≤ 5. Let O_K be the ring of algebraic integers of K. We say that K is monogenic if there exists some α ∈ O_K such that O_K = Z[α]. In this paper, we give some explicit conditions on a, b for which K is non-monogenic. We illustrate our results through examples.