Atomicity and boundedness of monotone Puiseux monoids

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 tra...

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Bibliographic Details
Published in:Semigroup forum 2018-06, Vol.96 (3), p.536-552
Main Authors: Gotti, Felix, Gotti, Marly
Format: Article
Language:English
Subjects:
Algebra
Atomic structure
Mathematics
Mathematics and Statistics
Monoids
Research Article
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Summary: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.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-017-9899-9