Elements with unique length factorization of a numerical semigroup generated by three consecutive numbers
Let S be the numerical semigroup generated by three consecutive numbers a,a +1,a +2, where a ¿ N, a = 3. We describe the elements of S whose factorizations have all the same length, as well as the set of factorizations of each of these elements. We give natural partitions of this subset of S in term...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/450261 |
| Acceso en línea: | https://hdl.handle.net/2117/450261 https://dx.doi.org/10.1007/s00233-025-10601-7 |
| Access Level: | acceso abierto |
| Palabra clave: | Semigroups Numerical semigroup Set of factorizations Unique length factorization Apéry set Betti element Semigrups Classificació AMS::20 Group theory and generalizations::20M Semigroups Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups |
| Sumario: | Let S be the numerical semigroup generated by three consecutive numbers a,a +1,a +2, where a ¿ N, a = 3. We describe the elements of S whose factorizations have all the same length, as well as the set of factorizations of each of these elements. We give natural partitions of this subset of S in terms of the length and the denumerant. By using Apéry sets and Betti elements we are able to extend some of these results to any general numerical semigroup S . These results provide a better understanding of the defining ideals associated with Moh’s examples and certain variants, which are related to the defining ideals of the semigroup rings k[t a ,t b ,t c ]. Moreover, the elements with unique length factorizations in S are useful to study the minimal generating sets of these ideals. |
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