2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145234In this paper, we extend the well-known Hilbert's syzygy theorem to the Gorenstein homological dimensions of rings. Also, we study the Gorenstein homological dimensions of direct products of rings. Our results generate examples of non-Noetherian rings of finite Gorenstein dimensions and infinite classical weak dimension.Commutative Algebratext