On the local k-elasticities of Puiseux monoids

DOI10.1142/S0218196718500662zbMath1506.20090arXiv1712.00837MaRDI QIDQ4629514

Marly Gotti

Publication date: 27 March 2019

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.00837

zbMATH Keywords

elasticityatomic monoidsfactorization theoryPuiseux monoidssystem of sets of lengthslocal elasticityunion of sets of lengths

Mathematics Subject Classification ID

Commutative semigroups (20M14) Ordered semigroups and monoids (06F05) Rational numbers as sums of fractions (11D68) Divisibility and factorizations in commutative rings (13A05) Arithmetic theory of semigroups (20M13)

Related Items (5)

Factorization invariants of the additive structure of exponential Puiseux semirings ⋮ Unnamed Item ⋮ Approximating length-based invariants in atomic Puiseux monoids ⋮ Factorization invariants of Puiseux monoids generated by geometric sequences ⋮ When Is a Puiseux Monoid Atomic?

Cites Work

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• Atomicity and boundedness of monotone Puiseux monoids
• The system of sets of lengths in Krull monoids under set addition
• A realization theorem for sets of lengths
• Numerical semigroups.
• Generalized sets of lengths
• How do elements really factor in \(\mathbb{Z}[\sqrt{-5}\)?]
• Full elasticity in atomic monoids and integral domains.
• Elasticity of factorization in number fields
• An arithmetic characterization of algebraic number fields with a given class group
• On the atomic structure of Puiseux monoids
• A Characterization of Algebraic Number Fields with Class Number Two

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