Finite homological dimension and primes associated to integrally closed ideals

DOI10.1090/S0002-9939-02-06436-5zbMath0995.13009OpenAlexW1727812930MaRDI QIDQ4539832

Futoshi Hayasaka, Shiro Goto

Publication date: 11 July 2002

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-02-06436-5

zbMATH Keywords

projective dimensionGorenstein dimensionintegrally closed idealGorensteinnessregularity of local ringSerre's condition \((S_1)\)

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Integral closure of commutative rings and ideals (13B22) Regular local rings (13H05)

Related Items (17)

On \({\mathfrak m}\)-full powers of parameter ideals ⋮ Testing for the Gorenstein property ⋮ Quasi-socle ideals and Goto numbers of parameters ⋮ Quasi-socle ideals in local rings with Gorenstein tangent cones ⋮ WeaklyG_K-Perfect and Integral Closure of Ideals ⋮ \(\mathfrak{m}\)-full and basically full ideals in rings of characteristic \(p\) ⋮ Completely -full ideals and componentwise linear ideals ⋮ The weak Lefschetz property for \(\mathfrak{m}\)-full ideals and componentwise linear ideals ⋮ Burch ideals and Burch rings ⋮ Effective normality criteria for algebras of linear type. ⋮ Maximally differential ideals of finite projective dimension ⋮ Quasi-socle ideals in Gorenstein numerical semigroup rings ⋮ Integrally Closed Modules and Their Divisors ⋮ Modules that detect finite homological dimensions ⋮ Tangent algebras ⋮ When is $R \ltimes I$ an almost Gorenstein local ring? ⋮ The $a$-invariant and Gorensteinness of graded rings associated to filtrations of ideals in regular local rings

Cites Work

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• Vanishing of \(Ext^ i_ R(M,R)\)
• Integral closedness of complete-intersection ideals
• On the integral closure of ideals
• Finite homological dimension and primes associated to integrally closed ideals. II.
• Ideals generated by \(R\)-sequences
• The $a$-invariant and Gorensteinness of graded rings associated to filtrations of ideals in regular local rings
• m-full ideals
• The syzygies of m-full ideals
• Tight closure in F-rational rings

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