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On the Depth of the Associated Graded Ring of an Ideal

✍ Scribed by Laura Ghezzi

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
161 KB
Volume
248
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let R be a local Cohen᎐Macaulay ring, let I be an R-ideal, and let G be the associated graded ring of I. We give an estimate for the depth of G when G fails to be Cohen᎐Macaulay. We assume that I has a small reduction number and sufficiently good residual intersection properties and satisfies local conditions on the depth of some powers. The main theorem unifies and generalizes several known results. We also give conditions that imply the Serre properties of the Ž .

πŸ“œ SIMILAR VOLUMES

Gorenstein Associated Graded Rings of An
Gorenstein Associated Graded Rings of Analytic Deviation Two Ideals
✍ Shiro Goto; Shin-ichiro Iai πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 146 KB

This paper studies the question of when the associated graded ring I = nβ‰₯0 I n /I n+1 of a certain ideal I in a local ring is Gorenstein. The main result implies, for example, that if A is a regular local ring, is a prime ideal in A with dim A/ = 2, and A/ is a complete intersection in codimension o