Measuring primality in numerical semigroups with embedding dimension three

Electronic version of an article published as Journal of Algebra and Its Applications, 15, 1, 2016, 1650007. DOI:10.1142/S0219498816500079 © World Scientific Publishing Company https://www.worldscientific.com/doi/abs/10.1142/S0219498816500079In this paper, we find the ω-value of the generators of any numerical semigroup with embedding dimension three. This allows us to determine all possible orderings of the ω-values of the generators. In addition, we relate the ω-value of the numerical semigroup to its catenary degree.The first and third authors received National Science Foundation support under DMS-1262897. The second author is supported by the projects MTM2010-15595, FQM-343, FQM-5849, NSF-1061366 and FEDER funds