Atomicity and Boundedness of Monotone Puiseux Monoids

Abstract

In this paper, we study the atomic structure of Puiseux monoids generated by monotone sequences. To understand this atomicity, it is often useful to know whether the monoid is bounded, in the sense that it has a bounded generating set. We provide necessary and sufficient conditions for 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.