Involve: A Journal of Mathematics

  • Involve
  • Volume 8, Number 4 (2015), 677-694.

When the catenary degree agrees with the tame degree in numerical semigroups of embedding dimension three

Pedro A. García-Sánchez and Caterina Viola

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We characterize numerical semigroups of embedding dimension three having the same catenary and tame degrees.

Article information

Involve, Volume 8, Number 4 (2015), 677-694.

Received: 13 July 2014
Revised: 20 August 2014
Accepted: 7 September 2014
First available in Project Euclid: 22 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20M13: Arithmetic theory of monoids
Secondary: 20M14: Commutative semigroups 13A05: Divisibility; factorizations [See also 13F15]

numerical semigroup catenary degree tame degree


García-Sánchez, Pedro A.; Viola, Caterina. When the catenary degree agrees with the tame degree in numerical semigroups of embedding dimension three. Involve 8 (2015), no. 4, 677--694. doi:10.2140/involve.2015.8.677.

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  • V. Blanco, P. A. García-Sánchez, and A. Geroldinger, “Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids”, Illinois J. Math. 55:4 (2011), 1385–1414.
  • S. T. Chapman, P. A. García-Sánchez, D. Llena, V. Ponomarenko, and J. C. Rosales, “The catenary and tame degree in finitely generated commutative cancellative monoids”, Manuscripta Math. 120:3 (2006), 253–264.
  • S. T. Chapman, P. A. García-Sánchez, and D. Llena, “The catenary and tame degree of numerical monoids”, Forum Math. 21:1 (2009), 117–129.
  • M. Delgado, P. A. García-Sánchez, and J. Morais, NumericalSgps: A package for numerical semigroups, 2013, hook \posturlhook.
  • C. Delorme, “Sous-monoï des d'intersection complète de $N$”, Ann. Sci. École Norm. Sup. $(4)$ 9:1 (1976), 145–154.
  • GAP: Groups, Algorithms, Programming –- a system for computational discrete algebra, The GAP Group, hook \posturlhook.
  • P. A. García-Sánchez and I. Ojeda, “Uniquely presented finitely generated commutative monoids”, Pacific J. Math. 248:1 (2010), 91–105.
  • P. A. García Sánchez, I. Ojeda, and J. C. Rosales, “Affine semigroups having a unique Betti element”, J. Algebra Appl. 12:3 (2013), 1250177.
  • A. Geroldinger and F. Halter-Koch, Non-unique factorizations: Algebraic, combinatorial and analytic theory, Pure and Applied Mathematics 278, Chapman & Hall/CRC, Boca Raton, FL, 2006.
  • J. Herzog, “Generators and relations of abelian semigroups and semigroup rings”, Manuscripta Math. 3 (1970), 175–193.
  • J. C. Rosales and P. A. García-Sánchez, Numerical semigroups, Developments in Mathematics 20, Springer, New York, 2009.