English

On the quotient of affine semigroups by a positive integer

Commutative Algebra 2024-02-20 v2 Number Theory

Abstract

This work delves into the {\it quotient of an affine semigroup by a positive integer}, exploring its intricate properties and broader implications. We unveil an {\it associated tree} that serves as a valuable tool for further analysis. Moreover, we successfully generalize several key irreducibility results, extending their applicability to the more general class of C\mathcal C-semigroup quotients. To shed light on these concepts, we introduce the novel notion of an {\it arithmetic variety of affine semigroups}, accompanied by illuminating examples that showcase its power.

Keywords

Cite

@article{arxiv.2402.09159,
  title  = {On the quotient of affine semigroups by a positive integer},
  author = {J. I. García-García and R. Tapia-Ramos and A. Vigneron-Tenorio},
  journal= {arXiv preprint arXiv:2402.09159},
  year   = {2024}
}