Asymptotic sequences

DOI10.1016/0021-8693(83)90099-6zbMath0522.13003OpenAlexW4212935727MaRDI QIDQ1055822

Louis J. jun. Ratliff

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0021-8693(83)90099-6

zbMATH Keywords

Cohen-Macaulay ringassociated primeNoetherianasymptotic sequenceasymptotic gradequasi-unmixed local ringR-sequencesgrade of idealintegral closure of ideal

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Commutative Noetherian rings and modules (13E05) Ideals and multiplicative ideal theory in commutative rings (13A15) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15)

Related Items (22)

Essential sequences and Rees rings ⋮ Essential sequences ⋮ Certain ideals for which \(I_ 1 \dots I_ g=I_ 1\cap \dots \cap I_ g\) ⋮ Form rings and projective equivalence ⋮ On the kernel of a monadic transformation ⋮ Sequences and \(\text{Ker}(R[X_1,\dots,X_g\to R[tI])\)] ⋮ Analytic spread and non-vanishing of asymptotic depth ⋮ Quintessential-modulated ideals ⋮ A Note on Asymptotic Prime Sequences ⋮ On the asymptotic sequences over an ideal ⋮ Bases of ideals and Rees valuation rings ⋮ On the grade and cograde of a Noetherian filtration ⋮ Asymptotic Sequences over Ideals and Projectively Equivalent Ideals with Respect to Modules ⋮ Grade functions and two classical theorems ⋮ Independent elements, unmixedness theorems, and asymptotic prime divisors ⋮ A Characterization of locally quasi-unmixed rings ⋮ Essential sequences over an ideal and essential cograde ⋮ Asymptotic sequences and Rees rings ⋮ Grade Schemes and Grade Functions ⋮ Asymptotic prime divisors and integral extension rings ⋮ Monoidal extensions of a locally quasi-unmixed UFD ⋮ U–essential prime divisors and sequences over an ideal

Cites Work

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• Integrally closed ideals and asymptotic prime divisors
• A brief survey and history of asymptotic prime divisors
• Independent elements, integrally closed ideals, and quasiunmixedness
• New characterizations of quasi-unmixed, unmixed, and Macaulay local domains
• On asymptotic prime divisors
• Independent elements and asymptotic sequences
• Locally quasi-unmixed Noetherian rings and ideals of the principal class
• Five theorems on Macaulay rings
• Some asymptotic properties of powers of ideals
• Note on a paper of Samuel concerning asymptotic properties of ideals
• Rings associated with ideals and analytic spread
• A theorem on integral closures of ideals in semi-local rings
• On Quasi-Unmixed Semi-Local Rings and the Altitude Formula
• On Quasi-Unmixed Local Domains, the Altitude Formula, and the Chain Condition for Prime Ideals, (I)
• Note on coefficient fields of complete local rings

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