Cohen-macaulay Modules and Holonomic Modules over Filtered Rings
نویسندگان
چکیده
We 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-dimM ≤ G-dimgrM and an equality gradeM = 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.
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