The prime ideals in every class contain arbitrary large truncated classes

TL;DR

This paper proves that in any class group of a number field, prime ideals contain arbitrarily large truncated ideal classes, revealing a deep structural property of algebraic number fields.

Contribution

It establishes a new result about the structure of prime ideals and their relation to truncated ideal classes in number fields.

Findings

Prime ideals in every class contain arbitrarily large truncated ideal classes

The result applies universally across all class groups of number fields

Provides insight into the distribution of prime ideals within class groups

Abstract

We prove that the prime ideals in every class of a number field contain arbitrary large truncated ideal classes.