On pseudo-Frobenius elements of submonoids of \mathbb {N}^d

• Autores: Juan Ignacio García García , Ignacio Ojeda Martínez de Castilla , José Carlos Rosales González , Alberto Vigneron-Tenorio
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 71, Fasc. 1, 2020, págs. 189-204
• Idioma: inglés
• DOI: 10.1007/s13348-019-00267-0
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• Resumen

  • In this paper we study those submonoids of \mathbb {N}^d 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 \mathbb {N}^d and using its pseudo-Frobenius elements we prove that the elements in the family are direct limits of affine semigroups.