2024-03-28T08:26:28Z
https://soar-ir.repo.nii.ac.jp/oai
oai:soar-ir.repo.nii.ac.jp:00011894
2022-12-14T04:14:04Z
1169:1170
COHEN-MACAULAY MODULES AND HOLONOMIC MODULES OVER FILTERED RINGS
Miyahara, H
Nishida, K
Gorenstein dimension
grade
filtered ring
Cohen-Macaulay module
holonomic module
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)
Taylor & Francis Inc.
2009
eng
journal article
AM
http://hdl.handle.net/10091/3891
https://soar-ir.repo.nii.ac.jp/records/11894
https://doi.org/10.1080/00927870802248605
10.1080/00927870802248605
0092-7872
AA00611371
Communications in Algebra
37
2
406
430
https://soar-ir.repo.nii.ac.jp/record/11894/files/cmh-rev-2.pdf
application/pdf
181.0 kB
2015-09-28