2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141214We study Gorenstein dimension and grade of a module $M$ over a filtered ring whose assosiated graded ring is a commutative Noetherian ring. An equality or an inequality between these invariants of a filtered module and its associated graded module is the most valuable property for an investigation of filtered rings. We prove an inequality G-dim$M\leq{G-dim gr}M$ and an equality ${\rm grade}M={\rm grade gr}M$, whenever Gorenstein dimension of ${\rm gr}M$ is finite (Theorems 2.3 and 2.8). We would say that the use of G-dimension adds a new viewpoint for studying filtered rings and modules. We apply these results to a filtered ring with a Cohen-Macaulay or Gorenstein associated graded ring and study a Cohen-Macaulay, perfect or holonomic module.21 pages, to appear in Communications in AlgebraRings and AlgebrasCommutative Algebra13C14, 13D05, 16E10, 16E30, 16E65, 16W70text