%0 Journal Article 
%A García García, Juan Ignacio
%A Tapia Ramos, Raquel
%A Vigneron Tenorio, Alberto
%T On the quotient of affine semigroups by a positive integer
%D 2024
%@ 1827-3491

%U http://hdl.handle.net/10498/36030
%X This work delves into the quotient of an affine semigroup by a positive integer, exploring its intricate properties and broader implications. We unveil an 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-semigroup quotients. To shed light on these concepts, we introduce the novel notion of an arithmetic variety of affine semigroups, accompanied by illuminating examples that showcase its power.
%K Affine semigroup
%K Arithmetic variety
%K C-semigroup
%K Frobenius element
%K Irreducibility
%K Quotient by a positive integer
%K Rooted tree
%~ Universidad de Cádiz