On the Buchsbaum property of associated graded rings

DOI10.1006/jabr.1998.7518zbMath0942.13002OpenAlexW1982623171MaRDI QIDQ1272467

Yukio Nakamura

Publication date: 21 August 2000

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1998.7518

zbMATH Keywords

associated graded ringBuchsbaum property\(d^+\)-sequences

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Local cohomology and commutative rings (13D45) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items (7)

Buchsbaumness in Rees modules associated to ideals of minimal multiplicity in the equi-\(\mathbb I\)-invariant case ⋮ Asymptotic Property of the 𝕀-Invariant of the Associated Graded Modules ⋮ Buchsbaumness of the associated graded rings of filtration ⋮ The associated graded modules of Buchsbaum modules with respect to \({\mathfrak m}\)-primary ideals in the equi-\(\mathbb{I}\)-invariant case ⋮ Buchsbaumness in the Rees modules associated to \(\mathfrak m\)-primary ideals in the one-dimensional case. ⋮ On the Buchsbaum associated graded modules with respect to \(\mathfrak m\)-primary ideals whose reduction numbers are at most one ⋮ Buchsbaumness of certain generalization of the associated graded modules in the equi-\(\mathbb I\)-invariant case

Cites Work

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• On Macaulayfication obtained by a blow-up whose center is an equi-multiple ideal. (With an appendix by Kikumichi Yamagishi)
• The theory of d-sequences and powers of ideals
• A tight closure approach to arithmetic Macaulayfication
• On relative regular sequences
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• Idealizations of maximal Buchsbaum modules over a Buchsbaum ring
• Form rings and regular sequences
• Toward a theory of generalized Cohen-Macaulay modules

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