On pseudo-Frobenius elements of submonoids of Nd

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URI: http://hdl.handle.net/10498/37314

DOI: 10.1007/s13348-019-00267-0

URL: https://link.springer.com/article/10.1007%2Fs13348-019-00267-0

ISSN: 0010-0757

ISSN: 2038-4815

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Autor/es
García García, Juan IgnacioAutoridad UCA; Ojeda, Ignacio; Rosales, Jose Carlos; Vigneron Tenorio, AlbertoAutoridad UCA
Fecha
2020
Departamento/s
Matemáticas
Fuente
Collectanea Mathematica - 2020, Vol. 71 pp.189–204
Resumen
In this paper we study those submonoids of Nd with a nontrivial pseudo-Frobenius set. In the affine case, we prove that they are the affine semigroups whose associated algebra over a field has maximal projective dimension possible. We prove that these semigroups are a natural generalization of numerical semigroups and, consequently, most of their invariants can be generalized. In the last section we introduce a new family of submonoids of Nd and using its pseudo-Frobenius elements we prove that the elements in the family are direct limits of affine semigroups.
Materias
Affine semigroups; Numerical semigroups; Frobenius elements; Pseudo-Frobenius elements; Apéry sets; Gluings; Free resolution; Irreducible semigroups
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