%0 Journal Article 
%A García García, Juan Ignacio
%A Moreno Frías, María Ángeles
%A Vigneron Tenorio, Alberto
%T Proportionally modular affine semigroups
%D 2017
%@ 0219-4988
%U http://hdl.handle.net/10498/35365
%X This 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, and we specialize when p = 2. For this
case, we also 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.
%K Affine semigroup
%K Buchsbaum ring
%K Cohen–Macaulay ring
%K Frobenius vector
%K Gorenstein ring
%K modular Diophantine inequalities
%K numerical monoid
%K numerical semigroup
%~ Universidad de Cádiz