Non-monogenity of some number fields generated by binomials or trinomials of prime-power degree

Abstract

Let [Formula: see text] be a prime number and [Formula: see text] be an algebraic number field with [Formula: see text] a root of an irreducible polynomial [Formula: see text] having integer coefficients. In this paper, we provide some explicit conditions involving only [Formula: see text] for which [Formula: see text] is non-monogenic. As an application, in the special case of [Formula: see text] and [Formula: see text], we show that if [Formula: see text] and [Formula: see text] divides [Formula: see text], then [Formula: see text] is not monogenic. We illustrate our results through examples.