Power integral bases in the family of simplest quartic fields

Abstract

Several authors have considered the infinite parametric family of simplest quartic fields $K_t=\mathbb Q(\xi)$. In this paper, we explicitly give all generators of power integral bases in the ring of integers $\mathbb Z_K$ of$K_t$ assuming that $t^2+16$is not divisible by an odd square. We use a well known general algorithm for calculating power integral bases in quartic fields.