2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75363Let $A$ be a $d\times n$ integer matrix whose column vectors generate the lattice $\Z^d$, and let $D(R_A)$ be the ring of differential operators on the affine toric variety defined by $A$. We show that the classification of $A$-hypergeometric systems and that of $\Z^d$-graded simple $D(R_A)$-modules (up to shift) are the same. We then show that the set of $\Z^d$-homogeneous primitive ideals of $D(R_A)$ is finite. Furthermore, we give conditions for the algebra $D(R_A)$ being simple.29 pagesRings and Algebras13N10; 13P99 (Primary), 16W35; 16S32 (Secondary)text