A Classification of Multiply Monogenic Quartic Orders

Shabnam Akhtari, Jaxon Shumaker

We study two-times monogenic quartic orders; i.e., those of the shape $\mathbb{Z}[\alpha ]=\mathbb{Z}[\beta ]$, with algebraic integers $\alpha$ and $\beta$ not $\mathbb{Z}$-equivalent. Two specific…