Algebraic integers of certain cubic extensions

Abstract

There is an extensive literature of cyclic number fields and cyclic fields of type, where and is a square free integer, for example [3], [4] and [5]. In this work, we present new results of the structure of the ring of algebraic integers of cubic number fields, that is, we explicitly give an integral basis of a cubic field in the form , where is a cube free integer, and its discriminant.