Research Article

Atomicity of positive monoids

Published in: Quaestiones Mathematicae
Volume 47 , issue 11 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 2177–2193
DOI: 10.2989/16073606.2024.2352875
Author(s): Scott T. Chapman Sam Houston State University, , Marly Gotti Data Science & Engineering, ,
Keywords: Primary: 20M13, Secondary: 06F05, 20M14, Positive monoids, Puiseux monoids, atomicity, factorization theory, ACCP, BF-monoids, FF-monoids,
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Abstract

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.
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