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COHEN-MACAULAY MODULES AND HOLONOMIC MODULES OVER FILTERED RINGS

Miyahara, Hiroaki and Nishida, Kenji COHEN-MACAULAY MODULES AND HOLONOMIC MODULES OVER FILTERED RINGS. In: 第12回代数学若手研究会, March 3--5, 2007., 千葉大学理学部.

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2007: 第12回代数学若手研究会

Abstract

We study Gorenstein dimension and grade of a module M over a ltered ring whose assosiated graded ring is a commutative Noetherian ring. An equality or an inequality between these invariants of a ltered module and its associated graded module is the most valuable property for an investigation of ltered rings. We prove an inequality G-dimM G-dim grM and an equality gradeM = grade grM, whenever Gorenstein dimension of grM is nite (Theorems 2.3 and 2.8). We would say that the use of G-dimension adds a new viewpoint for studying ltered rings and modules. We apply these results to a ltered ring with a Cohen-Macaulay or Gorenstein associated graded ring and study a Cohen-Macaulay, perfect or holonomic module.

Item Type:Conference or Workshop Item (UNSPECIFIED)
Uncontrolled Keywords:Gorenstein dimension, grade, filtered ring, Cohen-Macaulay module, holonomic module
Subjects:13-xx COMMUTATIVE RINGS AND ALGEBRAS
ID Code:1798