A characterization of weakly Krull monoid algebras

TL;DR

This paper characterizes when monoid algebras over a domain are weakly Krull, providing conditions that extend known results for Krull and generalized Krull properties, and applies these to affine monoid algebras.

Contribution

It offers a new characterization of weakly Krull monoid algebras and extends existing results on Krull properties in monoid algebra contexts.

Findings

Characterization of weakly Krull monoid algebras

Conditions for $D[S]$ to be Krull or generalized Krull

Identification of weakly Krull domains among affine monoid algebras

Abstract

Let $D$ be a domain and let $S$ be a torsion-free monoid whose quotient group satisfies the ascending chain condition on cyclic subgroups. We give a characterization of when the monoid algebra $D[S]$ is weakly Krull. As corollaries, we obtain the results on when $D[S]$ is Krull resp. generalized Krull, due to Chouinard resp. El Baghdadi and Kim. Furthermore, we deduce Chang's theorem on weakly factorial monoid algebras and we characterize the weakly Krull domains among the affine monoid algebras.