Integral Basis for quartic Kummer extensions over $\mathbb{Z}[{\hat{I}}^1]$

S. Venkataraman, Manisha V. Kulkarni

Let $K=\mathbb{Q}[{\hat{I}}^1]$ and $N=K[\sqrt[4]{\hat{I}}\pm ]$, $\hat{I}\pm \in \mathbb{Z}[{\hat{I}}^1]$, $alpha=f{g}^2{h}^3$, $f$, $g$, $h\in \mathbb{Z}[{\hat{I}}^1]$ are pairwise coprime and square free. Let ${\mathcal{O}}_N$ be t…