Year: 2024
Type: preprint
Abstract: Let $M$ be a commutative monoid. An element $d \in M$ is called a maximal common divisor of a nonempty subset $S$ of $M$ if $d$ is a common divisor of $S$ in $M$ and the only common divisors in $M$ of the set $\big\{ \frac{s}d : s \in S \big\}$ are the units of $M$. In this paper, we investigate the existence of maximal common divisors in rank-$1$ torsion-free commutative monoids, also known as Puiseux monoids. We also establish some connections between the existence of maximal common divisors and both atomicity and the ascending chain condition on principal ideals for the monoids we investigate here.
Source: arXiv (Cornell University)
Authors: Liang, Evin, Wang, Alexander, Zhong, Lerchen
Institution: Lexington City Schools
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403564496