Proportionally modular affine semigroups

J. I. García-García; M. A. Moreno-Frías; A. Vigneron-Tenorio

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arXiv · 1512.01513

Proportionally modular affine semigroups

J. I. García-García·M. A. Moreno-Frías·A. Vigneron-Tenorio

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Abstract

This work introduces a new kind of semigroup of $\N^p$ 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 $p=2$. 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) Fröbenius vectors are determinated.

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BibTeX RIS

J. I. García-García, M. A. Moreno-Frías, A. Vigneron-Tenorio. 2016-07-10. Proportionally modular affine semigroups. https://arxiv.org/abs/1512.01513

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