U–essential prime divisors and sequences over an ideal

DOI10.1017/S002776300000057XzbMath0569.13002OpenAlexW1958752405MaRDI QIDQ3686798

Daniel Katz, Louis J. jun. Ratliff

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1017/s002776300000057x

zbMATH Keywords

Rees ringideal in a Noetherian ringu- essential sequencesu-essential cogradeu-essential prime divisors

Mathematics Subject Classification ID

Commutative Noetherian rings and modules (13E05) Ideals and multiplicative ideal theory in commutative rings (13A15) Extension theory of commutative rings (13B02) Local rings and semilocal rings (13H99)

Related Items (21)

On linearly equivalent ideal topologies ⋮ On the relevant transform and the relevant component of an ideal ⋮ Quintasymptotic primes and four results of Schenzel ⋮ On the symbolic topology on an ideal ⋮ Certain ideals for which \(I_ 1 \dots I_ g=I_ 1\cap \dots \cap I_ g\) ⋮ On ideals whose adic and symbolic topologies are linearly equivalent ⋮ On the kernel of a monadic transformation ⋮ Bounds related to projective equivalence classes of ideals ⋮ Quintessential-modulated ideals ⋮ Two notes on ideal-transforms ⋮ Notes on projectively related ideals and residual division ⋮ Some results on top local cohomology modules with respect to a pair of ideals ⋮ On the asymptotic sequences over an ideal ⋮ Two asymptotic functions ⋮ On the grade and cograde of a Noetherian filtration ⋮ A bracket power characterization of analytic spread one ideals ⋮ Essential prime divisors and projectively equivalent ideals ⋮ Essential sequences and projective equivalence ⋮ Three Theorems on Form Rings ⋮ Sporadic and Irrelevant Prime Divisors ⋮ Equivalence of symbolic and adic topologies

Cites Work

• Essential sequences over an ideal and essential cograde
• On the asymptotic cograde of an ideal
• Asymptotic sequences
• Asymptotic prime divisors and integral extension rings
• Essential sequences and Rees rings
• Prime divisors, asymptotic R-sequences and unmixed local rings
• The asymptotic Ass
• On asymptotic prime divisors
• On the prime divisors of zero in form rings
• Notes on ideal covers and associated primes
• Locally quasi-unmixed Noetherian rings and ideals of the principal class
• On the Chain Problem of Prime Ideals
• A note on form rings and ideals
• 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 (II)

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