@article{oai:soar-ir.repo.nii.ac.jp:00011894,
author = {Miyahara, H and Nishida, K},
issue = {2},
journal = {Communications in Algebra},
month = {},
note = {We study Gorenstein dimension and grade of a module M over a filtered ring whose associated 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-dimM <= G-dim grM and an equality grade M = grade grM, whenever Gorenstein dimension of grM 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., Article, Communications in Algebra. 37(2):406-430 (2009)},
pages = {406--430},
title = {COHEN-MACAULAY MODULES AND HOLONOMIC MODULES OVER FILTERED RINGS},
volume = {37},
year = {2009}
}