Asymptotic <i>ω</i>-Primality of Finitely Generated Cancelative Commutative Monoids
The computation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-primality has been object of study, mainly, for numerical semigroups due...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/4/790 |
| _version_ | 1797619526691454976 |
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| author | Juan Ignacio García-García Daniel Marín-Aragón Alberto Vigneron-Tenorio |
| author_facet | Juan Ignacio García-García Daniel Marín-Aragón Alberto Vigneron-Tenorio |
| author_sort | Juan Ignacio García-García |
| collection | DOAJ |
| description | The computation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-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. |
| first_indexed | 2024-03-11T08:28:15Z |
| format | Article |
| id | doaj.art-4f12797bd5034e388e71685363f085ff |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T08:28:15Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4f12797bd5034e388e71685363f085ff2023-11-16T21:54:05ZengMDPI AGMathematics2227-73902023-02-0111479010.3390/math11040790Asymptotic <i>ω</i>-Primality of Finitely Generated Cancelative Commutative MonoidsJuan Ignacio García-García0Daniel Marín-Aragón1Alberto Vigneron-Tenorio2Departamento de Matemáticas/INDESS, Instituto Universitario para el Desarrollo Social Sostenible, Universidad de Cádiz, E-11510 Puerto Real, SpainDepartamento de Matemáticas, Universidad de Cádiz, E-11510 Puerto Real, SpainDepartamento de Matemáticas/INDESS, Instituto Universitario para el Desarrollo Social Sostenible, Universidad de Cádiz, E-11405 Jerez de la Frontera, SpainThe computation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>-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.https://www.mdpi.com/2227-7390/11/4/790asymptotic omega primalitynon-unique factorizationnumerical monoidnumerical semigroup |
| spellingShingle | Juan Ignacio García-García Daniel Marín-Aragón Alberto Vigneron-Tenorio Asymptotic <i>ω</i>-Primality of Finitely Generated Cancelative Commutative Monoids Mathematics asymptotic omega primality non-unique factorization numerical monoid numerical semigroup |
| title | Asymptotic <i>ω</i>-Primality of Finitely Generated Cancelative Commutative Monoids |
| title_full | Asymptotic <i>ω</i>-Primality of Finitely Generated Cancelative Commutative Monoids |
| title_fullStr | Asymptotic <i>ω</i>-Primality of Finitely Generated Cancelative Commutative Monoids |
| title_full_unstemmed | Asymptotic <i>ω</i>-Primality of Finitely Generated Cancelative Commutative Monoids |
| title_short | Asymptotic <i>ω</i>-Primality of Finitely Generated Cancelative Commutative Monoids |
| title_sort | asymptotic i ω i primality of finitely generated cancelative commutative monoids |
| topic | asymptotic omega primality non-unique factorization numerical monoid numerical semigroup |
| url | https://www.mdpi.com/2227-7390/11/4/790 |
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