The \(S_ 2\)-closure of a Rees algebra

DOI10.1007/BF03323133zbMath0777.13006OpenAlexW2028282161MaRDI QIDQ2366160

Sunsook Noh, Vasconcelos, Wolmer V.

Publication date: 29 June 1993

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03323133

zbMATH Keywords

minimal extensioncomplete intersectionRees algebracanonical modulefinite extensionNoetherian ringGorenstein local ring\(S_ 2\)\((S_{k+1})\)

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) Actions of groups on commutative rings; invariant theory (13A50) Rational and birational maps (14E05) Torsion theory for commutative rings (13D30)

Related Items

Cohen-Macaulay Rees algebras and degrees of polynomial relations, On multi-Rees algebras. With an appendix by Ngô Viêt Trung, Asymptotic prime ideals of \(S_{2}\)-filtrations, Reduction numbers, Rees algebras and Pfaffian ideals, On Rees algebras with a Gorenstein Veronese subring, On reduction exponents of ideals with Gorenstein formring, First coefficient ideals and the \(S_2\)-ification of a Rees algebra, Normal blow-ups and their expected defining equations, Degrees of multiplicity functions for equimultiple ideals, On the Depth of Blowup Algebras of Ideals with Analytic Deviation One, Unnamed Item, The Gorenstein and complete intersection properties of associated graded rings, On coefficient ideals

Uses Software

• Macaulay2

Cites Work

• Unnamed Item
• Unnamed Item
• Asymptotic prime divisors
• On the canonical module of the Rees algebra and the associated graded ring of an ideal
• Normal Rees algebras
• On the associated graded ring of an ideal
• Certain graded algebras are always Cohen-Macaulay
• Depth properties of Rees algebras and associated graded rings
• Ideals generated by \(R\)-sequences
• On an application of the Fitting invariants
• Der kanonische Modul eines Cohen-Macaulay-Rings. (The canonical moduls of a Cohen-Macaulay-ring)
• On the ubiquity of Gorenstein rings
• The ratliff-rush ideals in a noetherian ring
• Fibres formelles d'un anneau local noethérien
• Stable Ideals and Arf Rings