@misc{10498/26584,
year = {2022},
month = {4},
url = {http://hdl.handle.net/10498/26584},
abstract = {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.},
organization = {The authors thank the referees for their helpful observations. The authors were partially supported by Junta de Andalucia research group FQM-366. The first author was supported by the Programa Operativo de Empleo Juvenil 2014-2020, financed by the European Social Fund within the Youth Guarantee initiative. The second, third and fourth authors were partially supported by the project MTM2017-84890-P (MINECO/FEDER, UE), and the fourth author was partially supported by the project MTM2015-65764-C3-1-P (MINECO/FEDER, UE).},
publisher = {SPRINGER},
keywords = {Affine semigroup},
keywords = {C-semigroup},
keywords = {Embedding dimension},
keywords = {Gap of a semigroup},
keywords = {Generalized numerical semigroup},
keywords = {Irreducible semigroup},
title = {Characterizing affine C-semigroups},
doi = {10.1007/s11587-022-00693-6},
author = {Díaz-Ramírez, Juan de Dios and García García, Juan Ignacio and Marín Aragón, Daniel and Vigneron Tenorio, Alberto},
}