Atomicity and boundedness of monotone Puiseux monoids

By Felix Gotti, Marly Gotti. 2016

54 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1ba3a59ea0095fbfeacdc46b204cea7a007c08f1

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In Algebra and Number Theory

1. Felix Gotti
2. Scott T. Chapman
3. Marly Gotti
4. Alfred Geroldinger

In Computational Theory and Mathematics

1. Felix Gotti
2. Scott T. Chapman
3. Marly Gotti

Citations in the corpus

• Factorization invariants of Puiseux monoids generated by geometric sequences (2019, result): “Although no systematic study of the factorization of cyclic rational semirings has been carried out so far, in [31] the atomicity of Sr was first considered and classified in terms of the parameter r, as the next result indicates.”