Producción CientíficaThis work introduces a new kind of semigroup of Np called proportionally modular affine semigroup. These semigroups are defined by modular
Diophantine inequalities and they are a generalization of proportionally
modular numerical semigroups. We give an algorithm to compute their
minimal generating sets. We also specialize on the case p = 2. For this
case, we provide a faster algorithm to compute their minimal system of
generators, prove they are Cohen-Macaulay and Buchsbaum, and determinate their (minimal) Frobenius vectors. Besides, Gorenstein proportionally modular affine semigroups are characterized.Ministerio de Economía, Industria y Competitividad ( grants MTM2014-55367-P / MTM2015-65764- C3-1-P)Junta de Andalucía (FQM-366 / FQM-298
