# On the set of molecules of numerical and Puiseux monoids

@article{Gotti2020OnTS, title={On the set of molecules of numerical and Puiseux monoids}, author={Marly Gotti and Marcos M. Tirador}, journal={arXiv: Commutative Algebra}, year={2020} }

Additive submonoids of $\mathbb{Q}_{\ge 0}$, also known as Puiseux monoids, are not unique factorization monoids (UFMs) in general. Indeed, the only unique factorization Puiseux monoids are those generated by one element. However, even if a Puiseux monoid is not a UFM, it may contain nonzero elements having exactly one factorization. We call such elements molecules. Molecules were first investigated by W. Narkiewicz in the context of algebraic number theory. More recently, F. Gotti and the…

## One Citation

Factorizations in reciprocal Puiseux monoids

- Mathematics
- 2021

A Puiseux monoid is an additive submonoid of the real line consisting of rationals. We say that a Puiseux monoid is reciprocal if it can be generated by the reciprocals of the terms of a strictly…

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