Articles producció científica> Enginyeria Informàtica i Matemàtiques

Atomicity and density of Puiseux monoids

  • Identification data

    Identifier: imarina:9138872
    Authors:
    Bras-Amoros MGotti M
    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.
  • Others:

    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
    Link to the original source: https://www.tandfonline.com/doi/abs/10.1080/00927872.2020.1840574?journalCode=lagb20
    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
    Article's DOI: 10.1080/00927872.2020.1840574
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2021
    Publication Type: Journal Publications
  • Keywords:

    Algebra and Number Theory,Mathematics
    Puiseux monoid
    Increasing monoid
    Factorization
    Density
    Atomicity
    Atomically dense monoid
    Mathematics
    Matemática / probabilidade e estatística
    Algebra and number theory
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