The isomorphism problem for ideal class monoids of numerical semigroups García Sánchez, Pedro Abelardo Poset numerical semigroup Poset gapset numerical semigroup Ideal numerical semigroup Ideal class monoid The author is partially supported by the grant number ProyExcel_00868 (Proyecto de Excelencia de la Junta de Andalucía) and by the Junta de Andalucía Grant Number FQM--343. He also acknowledges financial support from the grant PID2022-138906NB-C21 funded by MICIU/AEI/10.13039/501100011033 and by ERDF "A way of making Europe'', and from the Spanish Ministry of Science and Innovation (MICINN), through the "Severo Ochoa and María de Maeztu Programme for Centres and Unities of Excellence'' (CEX2020-001105-M). Funding for open access charge: Universidad de Granada / CBUA. 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. 2024-04-10T12:17:23Z 2024-04-10T12:17:23Z 2024-04-10 info:eu-repo/semantics/article García Sánchez, Pedro Abelardo. The isomorphism problem for ideal class monoids of numerical semigroups. https://doi.org/10.48550/arXiv.2311.15265 https://hdl.handle.net/10481/90624 eng http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Atribución 4.0 Internacional