2026/08/04 by Shabnam Akhtari, Jaxon Shumaker
Mathematics · #math.NT
arxiv created 2026/08/04 · arxiv updated 2026/08/05
We study two-times monogenic quartic orders; i.e., those of the shape ℤ[α] = ℤ[β], with algebraic integers α and β not ℤ-equivalent. Two specific types, describing possible algebraic relation among monogenizers of two-times monogenic orders were defined by Bérczes, Evetrse, Győry, who proved under certain conditions on the Galois group of the normal closure of a given number field K, that there can be only finitely many two-times monogenic ℤ-orders in the ring of integers K which are not of these specific two types. In this article, we prove this fact for all quartic number fields.