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 = ℚ(ξ). In this paper, we explicitly give all generators of power integral bases in the ring of integers 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.

Keywords:

• Primary 11D57
• Secondary 11Y50
• power integral bases
• simplest quartic fields
• index form equations