On some norm inequalities and discriminant inequalities in CM-fields

Abstract

This is a shortened and slightly modified English version of our paper "Sur une classe des corps de nombres algébriques et ses applications", published in this journal in 1975; see Győry [10]. In that paper we studied an important class of number fields, namely the totally imaginary quadratic extensions of totally real number fields. We obtained among others some new norm inequalities and discriminant inequalities in such number fields. That time several different names were used in the literature for these number fields. This is the reason that the title of Győry [10] is not informative enough. Probably it is partly due to this fact that the results of [10] are less known. Nowadays, the name CM-field is generally accepted for the number fields under consideration. The purpose of this paper is to better call the attention to our norm inequalities and discriminant inequalities in CM-fields and to their applications.