RT info:eu-repo/semantics/article T1 On pseudo-Frobenius elements of submonoids of Nd A1 García García, Juan Ignacio A1 Ojeda, Ignacio A1 Rosales, José Carlos A1 Vigneron Tenorio, Alberto K1 Numerical semigroups K1 Semigrupos numéricos K1 Affine semigroups K1 Semigrupos afines K1 Pseudo-Frobenius number K1 Pseudo-número de Frobenius K1 Free resolutions K1 Resoluciones libres AB 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. PB Springer SN 2038-4815 YR 2020 FD 2020 LK http://uvadoc.uva.es/handle/10324/40730 UL http://uvadoc.uva.es/handle/10324/40730 LA eng NO Collectanea Mathematica, 2020, vol. 71. p. 189-204 NO Producción Científica DS UVaDOC RD 19-mar-2024