Proportionally modular affine semigroups
Commutative Algebra
2016-07-12 v2
Abstract
This work introduces a new kind of semigroup of called proportionally modular affine semigroup. These semigroups are defined by modular Diophantine inequalities and they are a generalization of proportionally modular numerical semigroups. We prove they are finitely generated and we give an algorithm to compute their minimal generating sets. We also specialise on the case . For this case, we provide a faster algorithm to compute their minimal system of generators and we prove they are Cohen-Macaulay and Buchsbaum. Besides, the Gorenstein property is charactized, and their (minimal) Fr\"obenius vectors are determinated.
Cite
@article{arxiv.1512.01513,
title = {Proportionally modular affine semigroups},
author = {J. I. García-García and M. A. Moreno-Frías and A. Vigneron-Tenorio},
journal= {arXiv preprint arXiv:1512.01513},
year = {2016}
}