Opened modular numerical semigroups.
The authors introduce the class of the opened modular numerical semigroups and obtain formulas for the Frobenius number, the singularity degree and the type of these semigroups. This continues earlier work of the authors and García-Sánchez [see for instance \textit{J. C. Rosales, P. A. García-Sánchez, J. I. García-García, J. M. Urbano-Blanco}, J. Number Theory 103, No. 2, 281-294 (2003; Zbl 1039.20036); \textit{J. C. Rosales, J. M. Urbano-Blanco}, Semigroup Forum 72, No. 3, 362-374 (2006; Zbl 1103.20057)]. Furthermore, a characterization of irreducible proportionally modular numerical semigroups in terms of opened modular numerical semigroups is established.
scientific article; zbMATH DE number 5115344
scientific article