On conductor submonoids of factorial monoids

TL;DR

This paper investigates the algebraic and arithmetic properties of conductor submonoids within factorial monoids, confirming several conjectures and extending previous research in the area.

Contribution

It provides new insights into the structure of conductor submonoids and proves multiple conjectures related to their properties.

Findings

Confirmed several conjectures about conductor submonoids.

Established new algebraic properties of submonoids in factorial monoids.

Extended previous work by Baeth, Cisto, et al.

Abstract

We study algebraic and arithmetic properties of submonoids (resp. subrings) of factorial monoids (resp. factorial domains) whose non-invertible elements all lie in the conductor. This continues earlier work of Baeth, Cisto, et al.. On our way we answer several conjectures, formulated in their papers in the affirmative ([1,Conjecture 4.16] and [6, Conjectures 2.3 and 2.10, and Section 9]).