2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145384In 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 product of rings, which gives examples of non-Noetherian rings of finite Gorenstein dimensions and infinite classical weak dimension.Commutative AlgebraGlobal Gorenstein dimensions of polynomial rings and of direct product of ringstext