The isomorphism problem for ideal class monoids of numerical semigroups
Identificadores
URI: https://hdl.handle.net/10481/90624Metadatos
Mostrar el registro completo del ítemMateria
Poset numerical semigroup Poset gapset numerical semigroup Ideal numerical semigroup Ideal class monoid
Fecha
2024-04-10Referencia bibliográfica
García Sánchez, Pedro Abelardo. The isomorphism problem for ideal class monoids of numerical semigroups. https://doi.org/10.48550/arXiv.2311.15265
Patrocinador
Junta de Andalucía ProyExcel_00868 FQM--343; MICIU/AEI/10.13039/501100011033 PID2022-138906NB-C21; ERDF "A way of making Europe''; Spanish Ministry of Science and Innovation CEX2020-001105-M; Universidad de Granada / CBUAResumen
From any poset isomorphic to the poset of gaps of a numerical semigroup S with the order induced by S, one can recover S. As an application, we prove that two different numerical semigroups cannot have isomorphic posets (with respect to set inclusion) of ideals whose minimum is zero. We also show that given two numerical semigroups S and T, if their ideal class monoids are isomorphic, then S must be equal to T.