On the distribution of prime divisors in Krull monoid algebras

TL;DR

This paper proves that in Krull monoid algebras, each class of the divisor class group contains infinitely many prime divisors, filling gaps in previous partial results.

Contribution

It provides a complete proof that every class in the divisor class group of a Krull monoid algebra has infinitely many prime divisors, resolving open gaps in prior research.

Findings

Each class contains infinitely many prime divisors

Complete proof of a longstanding conjecture

Addresses gaps in previous literature

Abstract

In the present work, we prove that every class of the divisor class group of a Krull monoid algebra contains infinitely many prime divisors. Several attempts to this result have been made in the literature so far, unfortunately with open gaps. We present a complete proof of this fact.