The catenary and tame degree of numerical monoids generated by generalized arithmetic sequences

DOI10.1515/form.2011.078zbMath1252.20057arXiv1001.1646OpenAlexW2963872705MaRDI QIDQ2890546

M. Omidali

Publication date: 11 June 2012

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.1646

zbMATH Keywords

numbers of generatorsnumerical semigroupsnumerical monoidscatenary degreegeneralized arithmetic sequencestame degree

Mathematics Subject Classification ID

Commutative semigroups (20M14) Free semigroups, generators and relations, word problems (20M05) Special sequences and polynomials (11B83) Arithmetic theory of semigroups (20M13)

Related Items (23)

Numerical semigroups generated by quadratic sequences ⋮ The monotone catenary degree of Krull monoids. ⋮ Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids. ⋮ THE CATENARY AND TAME DEGREES ON A NUMERICAL MONOID ARE EVENTUALLY PERIODIC ⋮ A characterization of arithmetical invariants by the monoid of relations. ⋮ An algorithm to compute \(\omega\)-primality in a numerical monoid. ⋮ Unnamed Item ⋮ The catenary degree of Krull monoids. I ⋮ Factorization invariants in numerical monoids ⋮ On strongly primary monoids and domains ⋮ Factorization properties of Leamer monoids. ⋮ On arithmetical numerical monoids with some generators omitted ⋮ On the arithmetic of stable domains ⋮ An improved algorithm to compute the \(\omega\)-primality ⋮ Measuring primality in numerical semigroups with embedding dimension three ⋮ On the arithmetic of tame monoids with applications to Krull monoids and Mori domains. ⋮ A realization theorem for sets of lengths in numerical monoids ⋮ Numerical Semigroups on Compound Sequences ⋮ Numerical semigroups, polyhedra, and posets. II: Locating certain families of semigroups ⋮ Local and Global Tameness in Krull Monoids ⋮ THE CATENARY DEGREE OF KRULL MONOIDS II ⋮ A characterization of arithmetical invariants by the monoid of relations. II: The monotone catenary degree and applications to semigroup rings. ⋮ On the atomic structure of Puiseux monoids

Uses Software

• GAP
• numericalsgps

Cites Work

• Local tameness of \(v\)-Noetherian monoids.
• Full elasticity in atomic monoids and integral domains.
• The catenary and tame degree in finitely generated commutative cancellative monoids.
• Presentations of finitely generated cancellative commutative monoids and nonnegative solutions of systems of linear equations.
• On Numerical Semigroups Generated by Generalized Arithmetic Sequences
• ON DELTA SETS OF NUMERICAL MONOIDS
• The catenary and tame degree of numerical monoids
• On the Type and the Minimal Presentation of Certain Numerical Semigroups
• On the linear diophantine problem of Frobenius.

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