Atomicity and boundedness of monotone Puiseux monoids
- 105 Downloads
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.
KeywordsPuiseux monoids Atomic structure Numerical semigroups Atomic monoids Primary Puiseux monoids Commutative semigroups
While working on this paper, the first author was supported by the UC Berkeley Chancellor Fellowship, and the second author was under the University of Florida Mathematics Department Fellowship. With pleasure both authors thank Scott Chapman and the anonymous referee for valuable suggestions which resulted in an improvement of this paper.
- 1.Apostol, T.: Introduction to Analytic Number Theory, Undergraduate Texts in Mathematics. Springer, New York (1976)Google Scholar
- 3.Clark, P.: Dirichlet’s Theorem on Primes in Arithmetic Progressions, University of Georgia. http://math.uga.edu/pete/4400FULL.pdf
- 9.Gotti, F.: On the atomic structure of Puiseux monoids. J. Algebra Appl. 16, 1750126 (2017). [arXiv:1607.01731]