%0 Journal Article 
%A Díaz-Ramírez, Juan de Dios
%A García García, Juan Ignacio
%A Marín Aragón, Daniel
%A Vigneron Tenorio, Alberto
%T Characterizing affine C-semigroups
%D 2022
%@ 0035-5038

%U http://hdl.handle.net/10498/26584
%X Let C subset of N-p be a finitely generated integer cone and S subset of C be an affine semigroup such that the real cones generated by C and by S are equal. The semigroup S is called C-semigroup if C \ S is a finite set. In this paper, we characterize the C-semigroups from their minimal generating sets, and we give an algorithm to check if S is a C-semigroup and to compute its set of gaps. We also study the embedding dimension of C-semigroups obtaining a lower bound for it, and introduce some families of C-semigroups whose embedding dimension reaches our bound. In the last section, we present a method to obtain a decomposition of a C-semigroup into irreducible C-semigroups.
%K Affine semigroup
%K C-semigroup
%K Embedding dimension
%K Gap of a semigroup
%K Generalized numerical semigroup
%K Irreducible semigroup
%~ Universidad de Cádiz