The Furstenberg property in Puiseux monoids

Autor:	Lin, Andrew, Rabinovitz, Henrick, Zhang, Qiao
Rok vydání:	2023
Předmět:	Mathematics - Commutative Algebra Primary: 20M13 11Y05 Secondary: 20M14 06F05
Druh dokumentu:	Working Paper
Popis:	Let $M$ be a commutative monoid. The monoid $M$ is called atomic if every non-invertible element of $M$ factors into atoms (i.e., irreducible elements), while $M$ is called a Furstenberg monoid if every non-invertible element of $M$ is divisible by an atom. Additive submonoids of $\mathbb{Q}$ consisting of nonnegative rationals are called Puiseux monoids, and their atomic structure has been actively studied during the past few years. The primary purpose of this paper is to investigate the property of being Furstenberg in the context of Puiseux monoids. In this direction, we consider some properties weaker than being Furstenberg, and then we connect these properties with some atomic results which have been already established for Puiseux monoids. Comment: 17 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.12372 Zobrazit plný text záznamu View this record from Arxiv