Computation of the \(\omega\)-primality and asymptotic \(\omega\)-primality with applications to numerical semigroups.

DOI10.1007/s11856-014-1144-6zbMath1337.20067arXiv1307.5807OpenAlexW2159091683MaRDI QIDQ2339617

Alberto Vigneron-Tenorio, M. A. Moreno-Frías, Juan Ignacio García García

Publication date: 2 April 2015

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.5807

zbMATH Keywords

numerical semigroupsnon-unique factorizationsfactorization theoryfactorization lengthsomega-primalityArchimedean monoidsfinitely generated atomic monoids

Mathematics Subject Classification ID

Commutative semigroups (20M14) Free semigroups, generators and relations, word problems (20M05) Divisibility and factorizations in commutative rings (13A05) Arithmetic theory of semigroups (20M13)

Related Items (10)

Factorization invariants of the additive structure of exponential Puiseux semirings ⋮ Factorization length distribution for affine semigroups. I: Numerical semigroups with three generators ⋮ The computation of factorization invariants for affine semigroups ⋮ Factorization invariants in numerical monoids ⋮ On dynamic algorithms for factorization invariants in numerical monoids ⋮ On divisor-closed submonoids and minimal distances in finitely generated monoids ⋮ An improved algorithm to compute the \(\omega\)-primality ⋮ \(\omega \)-primality in arithmetic Leamer monoids ⋮ On factorization invariants and Hilbert functions ⋮ Factorization invariants of Puiseux monoids generated by geometric sequences

Uses Software

• numericalsgps
• OmegaPrimality

Cites Work

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• Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids.
• An algorithm to compute \(\omega\)-primality in a numerical monoid.
• Atomic commutative monoids and their elasticity.
• On a generalization of the exchange property to modules with semilocal endomorphism rings.
• Local tameness of \(v\)-Noetherian monoids.
• On commutative, nonpotent archimedean semigroups
• HOW FAR IS AN ELEMENT FROM BEING PRIME?
• Chains of factorizations in weakly Krull domains
• FACTORIZATION INVARIANTS IN HALF-FACTORIAL AFFINE SEMIGROUPS
• numericalsgps, a GAP package for numerical semigroups
• Irreducible ideals of finitely generated commutative monoids

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