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arXiv · 2402.09159

On the quotient of affine semigroups by a positive integer

J. I. García-García·R. Tapia-Ramos·A. Vigneron-Tenorio
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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 $\mathcal C$-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.

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J. I. García-García, R. Tapia-Ramos, A. Vigneron-Tenorio. 2024-02-14. On the quotient of affine semigroups by a positive integer. https://arxiv.org/abs/2402.09159

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