Quartic number fields and prime ideal

Abstract

Based on Newton polygon techniques, for every prime integer p, a p-integral basis of ℤ_K, and the factorization of the principal ideal pℤ_K into prime ideals of ℤ_K are given, where K is a quintic number field defined by an irreducible trinomial X⁵ + aX² + b ∈ ℤ[X].