Atomicity of Positive Monoids

An additive submonoid of the nonnegative cone of the real line is called a positive monoid. Positive monoids consisting of rational numbers (also known as Puiseux monoids) have been the subject of several recent papers. Moreover, those generated by a geometric sequence have also received a great dea...

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Bibliographic Details
Published in:arXiv.org 2021-08
Main Authors: Chapman, Scott T, Gotti, Marly
Format: Article
Language:English
Subjects:
Monoids
Numbers
Online Access:Get full text
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Summary:An additive submonoid of the nonnegative cone of the real line is called a positive monoid. Positive monoids consisting of rational numbers (also known as Puiseux monoids) have been the subject of several recent papers. Moreover, those generated by a geometric sequence have also received a great deal of recent attention. Our purpose is to survey many of the recent advances regarding positive monoids, and we provide numerous examples to illustrate the complexity of their atomic and arithmetic structures.
ISSN:2331-8422