A Note on Relative Power Integral Basis of Number Fields Defined by $$x^n + ax^m - b$$

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].