Integral Basis for quartic Kummer extensions over $\mathbb{Z}[\iota ]$

S. Venkataraman, Manisha V. Kulkarni

Let $K=\mathbb{Q}[\iota ]$ and $N=K[\sqrt[4]{\alpha }]$, $\alpha \in \mathbb{Z}[\iota ]$, $alpha=f{g}^2{h}^3$, $f$, $g$, $h\in \mathbb{Z}[\iota ]$ are pairwise coprime and square free. Let ${\mathcal{O}}_N$ be the ri…