Good ideals in Gorenstein local rings

DOI10.1090/S0002-9947-00-02694-5zbMath0966.13002OpenAlexW2011067851MaRDI QIDQ2706614

Shin-ichiro Iai, Shiro Goto, Kei- ichi Watanabe

Publication date: 20 March 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-00-02694-5

zbMATH Keywords

Cohen-Macaulay ringGorenstein ringassociated graded ringRees algebralocal cohomology\(a\)-invariantgood idealGorenstein graded algebrasrational local rings

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

Good ideals and \(p_g\)-ideals in two-dimensional normal singularities ⋮ Ulrich ideals and 2-AGL rings ⋮ Reflexive modules over the endomorphism algebras of reflexive trace ideals ⋮ A characterization of two-dimensional rational singularities via core of ideals ⋮ The strong Rees property of powers of the maximal ideal and Takahashi-Dao's question ⋮ Hilbert coefficients and the Gorenstein property of the associated graded ring. ⋮ Almost Gorenstein Rees algebras of pg-ideals, good ideals, and powers of the maximal ideals ⋮ Ulrich ideals and modules ⋮ The structure of Ulrich ideals in hypersurfaces ⋮ Good ideals in Gorenstein local rings obtained by idealization ⋮ Rees algebras of F-regular type. ⋮ The almost Gorenstein Rees algebras of parameters ⋮ Good ideals in Artinian Gorenstein local rings obtained by idealization. ⋮ The multiplicity and the number of generators of an integrally closed ideal ⋮ Correspondence between trace ideals and birational extensions with application to the analysis of the Gorenstein property of rings ⋮ Ulrich ideals in numerical semigroup rings of small multiplicity ⋮ Complete intersection in overrings of a certain one-dimensional Gorenstein graded local ring ⋮ Gorenstein associated graded rings of analytic deviation two ideals.

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