• Corpus ID: 221266617

On the set of molecules of numerical and Puiseux monoids

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