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Estimates on the Depth of the Associated Graded Ring

✍ Scribed by Anna Guerrieri; Maria Evelina Rossi

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
155 KB
Volume
211
Category
Article
ISSN
0021-8693

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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

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Let I be an α’Š-primary ideal in a Buchsbaum local ring A, α’Š . In this paper, we investigate the Buchsbaum property of the associated graded ring of I when the equality I 2 s α’Ž I holds for some minimal reduction α’Ž of I. However, the Buchsbaum property does not always follow even if I 2 s α’Ž I. So we gi