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Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids

Víctor Blanco; Pedro A. García-Sánchez; Alfred Geroldinger — 2010

Actes des rencontres du CIRM

Arithmetical invariants—such as sets of lengths, catenary and tame degrees—describe the non-uniqueness of factorizations in atomic monoids.We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.

Numerical semigroups with a monotonic Apéry set

José Carlos Rosales; Pedro A. García-Sánchez; Juan Ignacio García-García; M. B. Branco — 2005

Czechoslovak Mathematical Journal

We study numerical semigroups $S$ with the property that if $m$ is the multiplicity of $S$ and $w (i)$ is the least element of $S$ congruent with $i$ modulo $m$ , then $0 < w (1) < \dots < w (m - 1)$ . The set of numerical semigroups with this property and fixed multiplicity is bijective with an affine semigroup and consequently it can be described by a finite set of parameters. Invariants like the gender, type, embedding dimension and Frobenius number are computed for several families of this kind of numerical semigroups.

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