2024/02/14 by García-García, J. I., Tapia-Ramos, R., Vigneron-Tenorio, A. · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2402.09159
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.