Abstract:
Let $K$ be a number field with ring of algebraic integers $R$. Let $L=K(\alpha)$ be a finite extension of $K$ where $\alpha$ is a root of an irreducible polynomial of the type $f(x)=x^n+ax^m-b$ belonging to $R[x]$ ($n, m\in \mathbb{N}$ and $n>m $). In this paper, we give a set of necessary and sufficient conditions to study the monogenity of $L$ over $K$. We also provide a class of finite separable extensions $L$ of $K$ for which $L/K$ is not monogenic. Our results extend the one given in [1].
