Author, as appears in the article.: Bras-Amoros M; Gotti M
Department: Enginyeria Informàtica i Matemàtiques
URV's Author/s: Bras Amoros, Maria
Keywords: Puiseux monoid Increasing monoid Factorization Density Atomicity Atomically dense monoid
Abstract: © 2020 Taylor & Francis Group, LLC. A Puiseux monoid is an additive submonoid consisting of non-negative rationals. Although the operation of addition is continuous with respect to the standard topology, the set of irreducibles of a Puiseux monoid is, in general, difficult to describe. Here, we use topological density to understand how much a Puiseux monoid, as well as its set of irreducibles, spread throughout the real line. First, we separate Puiseux monoids according to their density, and we characterize monoids in each of these classes in terms of generating sets and sets of irreducibles. Then we study the density of the difference group, the root closure, and the conductor semigroup of a Puiseux monoid. Finally, we prove that every Puiseux monoid generated by a strictly increasing sequence of rationals is nowhere dense in the real line and has empty conductor.
Thematic Areas: Mathematics Matemática / probabilidade e estatística Algebra and number theory
licence for use: https://creativecommons.org/licenses/by/3.0/es/
Author's mail: maria.bras@urv.cat
Author identifier: 0000-0002-3481-004X
Record's date: 2024-07-27
Papper version: info:eu-repo/semantics/acceptedVersion
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Papper original source: Communications In Algebra. (4): 1560-1570
APA: Bras-Amoros M; Gotti M (2021). Atomicity and density of Puiseux monoids. Communications In Algebra, (4), 1560-1570. DOI: 10.1080/00927872.2020.1840574
Entity: Universitat Rovira i Virgili
Journal publication year: 2021
Publication Type: Journal Publications
Repositori URV