Atomicity and boundedness of monotone Puiseux monoids
Felix Gotti, Marly Gotti
TL;DR
This paper investigates the atomic structure of monotone Puiseux monoids, establishing conditions for atomicity and boundedness transfer, and classifies atomic structures in specific subfamilies.
Contribution
It provides necessary and sufficient conditions for atomicity and boundedness transfer in monotone Puiseux monoids and classifies atomic structures in two special subfamilies.
Findings
Conditions for atomicity transfer are established.
Conditions for boundedness transfer are identified.
Complete classification of atomic structures in two subfamilies.
Abstract
In this paper, we study the atomic structure of Puiseux monoids generated by monotone sequences. To understand this atomic structure, it is often useful to know whether the monoid has a bounded generating set. We provide necessary and sufficient conditions for the atomicity and boundedness to be transferred from a monotone Puiseux monoid to all its submonoids. Finally, we present two special subfamilies of monotone Puiseux monoids and fully classify their atomic structure.
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