Asymptotic ω -Primality of Finitely Generated Cancelative Commutative Monoids

Juan Ignacio García-García, Daniel Marín-Aragón () and Alberto Vigneron-Tenorio
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Juan Ignacio García-García: Departamento de Matemáticas/INDESS, Instituto Universitario para el Desarrollo Social Sostenible, Universidad de Cádiz, E-11510 Puerto Real, Spain
Daniel Marín-Aragón: Departamento de Matemáticas, Universidad de Cádiz, E-11510 Puerto Real, Spain
Alberto Vigneron-Tenorio: Departamento de Matemáticas/INDESS, Instituto Universitario para el Desarrollo Social Sostenible, Universidad de Cádiz, E-11405 Jerez de la Frontera, Spain

Mathematics, 2023, vol. 11, issue 4, 1-10

Abstract: The computation of ω -primality has been object of study, mainly, for numerical semigroups due to its multiple applications to the Factorization Theory. However, its asymptotic version is less well known. In this work, we study the asymptotic ω -primality for finitely generated cancelative commutative monoids. By using discrete geometry tools and the Python programming language we present an algorithm to compute this parameter. Moreover, we improve the proof of a known result for numerical semigroups.

Keywords: asymptotic omega primality; non-unique factorization; numerical monoid; numerical semigroup (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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