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Atomicity and density of Puiseux monoids

  • Dades identificatives

    Identificador: imarina:9138872
    Autors:
    Bras-Amoros MGotti M
    Resum:
    © 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.
  • Altres:

    Autor segons l'article: Bras-Amoros M; Gotti M
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: Bras Amoros, Maria
    Paraules clau: Puiseux monoid Increasing monoid Factorization Density Atomicity Atomically dense monoid
    Resum: © 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.
    Àrees temàtiques: Mathematics Matemática / probabilidade e estatística Algebra and number theory
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: maria.bras@urv.cat
    Identificador de l'autor: 0000-0002-3481-004X
    Data d'alta del registre: 2024-07-27
    Versió de l'article dipositat: info:eu-repo/semantics/acceptedVersion
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referència a l'article segons font original: Communications In Algebra. (4): 1560-1570
    Referència de l'ítem segons les normes 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
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2021
    Tipus de publicació: Journal Publications
  • Paraules clau:

    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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