On the Gorensteinness of Rees algebras over local rings

DOI10.1017/S0027763000000489zbMath0585.13014OpenAlexW1534436196MaRDI QIDQ3710619

Shin S. Ikeda

Publication date: 1986

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0027763000000489

zbMATH Keywords

Cohen-Macaulay ringGorenstein ringRees algebragraded ringNoetherian local ringlocal dualitycanonical modulesassociated

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) (13D03) Ideals and multiplicative ideal theory in commutative rings (13A15)

Related Items (21)

The almost Gorenstein Rees algebras over two-dimensional regular local rings ⋮ Action of finite groups on Rees algebras and Gorensteinness in invariant subrings ⋮ On multi-Rees algebras. With an appendix by Ngô Viêt Trung ⋮ Quasi-socle ideals and Goto numbers of parameters ⋮ Quasi-socle ideals in local rings with Gorenstein tangent cones ⋮ On the Gorenstein property of Rees algebras ⋮ On Rees algebras with a Gorenstein Veronese subring ⋮ Good ideals in Gorenstein local rings ⋮ Hilbert coefficients and the Gorenstein property of the associated graded ring. ⋮ On a-invariant formulas ⋮ The Gorenstein property of the associated graded rings of powers of an ideal ⋮ Cohen-Macaulay and Gorenstein property of Rees algebras of non-singular equimultiple prime ideals ⋮ Rees algebras of non-singular equimultiple prime ideals ⋮ The almost Gorenstein Rees algebras of parameters ⋮ Unnamed Item ⋮ Buchsbaumness in Rees algebras associated to ideals of minimal multiplicity ⋮ Embeddings of certain graded rings into their canonical modules ⋮ Gorenstein graded rings associated to ideals ⋮ On the Cohen-Macaulay and Gorenstein properties of multigraded Rees algebras ⋮ On the Gorenstein property of form rings ⋮ The $a$-invariant and Gorensteinness of graded rings associated to filtrations of ideals in regular local rings

Cites Work

• Injective modules over Noetherian rings
• Some basic results on canonical modules
• On graded rings. I
• A conjecture of Nagata on graded Cohen-Macaulay rings
• On the ubiquity of Gorenstein rings
• The Cohen-Macaulayness of the Rees algebras of local rings
• Remarks on lifting of Cohen-Macaulay property
• Verallgemeinerte COHEN-MACAULAY-Moduln

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