2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95356In this paper we discuss minimal primes over permanental ideals of generic matrices. We give a complete list of the minimal primes over ideals of 3 x 3 permanents of a generic matrix, and show that there are monomials in the ideal of maximal permanents of a d x 2d-1 matrix if the characteristic of the ground field is sufficiently large. We also discuss the Alon-Jaeger-Tarsi Conjecture, using our results and techniques to strenthen the previously known results.22 PagesCommutative AlgebraCombinatorics13P10,13F20text