Approximating length-based invariants in atomic Puiseux monoids

A numerical monoid is a cofinite additive submonoid of the nonnegative integers, while a Puiseux monoid is an additive submonoid of the nonnegative cone of the rational numbers. Using that a Puiseux monoid is an increasing union of copies of numerical monoids, we prove that some of the factorization...

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Bibliographic Details
Date:2022
Main Author: Polo, H.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2022
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Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1760
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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Summary:A numerical monoid is a cofinite additive submonoid of the nonnegative integers, while a Puiseux monoid is an additive submonoid of the nonnegative cone of the rational numbers. Using that a Puiseux monoid is an increasing union of copies of numerical monoids, we prove that some of the factorization invariants of these two classes of monoids are related through a limiting process. This allows us to extend results from numerical to Puiseux monoids. We illustrate the versatility of this technique by recovering various known results about Puiseux monoids.