%0 Journal Article 
%A García García, Juan Ignacio
%A Ojeda, Ignacio
%A Rosales, Jose Carlos
%A Vigneron Tenorio, Alberto
%T On pseudo-Frobenius elements of submonoids of Nd
%D 2020
%@ 0010-0757

%U http://hdl.handle.net/10498/37314
%X 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.
%K Affine semigroups
%K Numerical semigroups
%K Frobenius elements
%K Pseudo-Frobenius elements
%K Apéry sets
%K Gluings
%K Free resolution
%K Irreducible semigroups
%~ Universidad de Cádiz