The isomorphism problem for ideal classmonoids of numerical semigroups

García Sánchez, Pedro Abelardo

doi:10.1007/s00233-024-10429-7

s00233-024-10429-7.pdf (318.9Kb)

Identificadores

URI: https://hdl.handle.net/10481/93397

DOI: 10.1007/s00233-024-10429-7

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Editorial

Springer

Materia

Poset numerical semigroup

Poset gapset numerical semigroup

Ideal of numerical semigroup

Date

2024-04-16

Referencia bibliográfica

García Sánchez, P.A. Semigroup Forum (2024) 108:365–376. [https://doi.org/10.1007/s00233-024-10429-7]

Sponsorship

ProyExcel_00868 (Proyecto de Excelencia de la Junta de Andalucía); Junta de Andalucía grant number FQM– 343; PID2022-138906NB-C21 funded by MICIU/AEI/10.13039/501100011033; ERDF “A way of making Europe”, and from the Spanish Ministry of Science and Innovation (MICINN); “Severo Ochoa and María de Maeztu Programme for Centres and Unities of Excellence” (CEX2020-001105-M)

Abstract

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 .

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