On the grade and cograde of a Noetherian filtration

DOI10.1017/S0027763000003524zbMath0727.13003MaRDI QIDQ3349009

Louis J. jun. Ratliff, J. S. Okon

Publication date: 1991

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

zbMATH Keywords

analytic spreadNoetherian ringintegral closureasymptotic prime divisorsessential prime divisorNoetherian filtrationsasymptotic cogradequintasymptotic prime divisorquintessential prime divisor

Mathematics Subject Classification ID

Commutative Noetherian rings and modules (13E05) Ideals and multiplicative ideal theory in commutative rings (13A15) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Integral dependence in commutative rings; going up, going down (13B21) Regular local rings (13H05)

Related Items (1)

Analytic spread of nitrations, asymptotic nature and some stability properties

Cites Work

• Essential prime divisors and projectively equivalent ideals
• Essential sequences over an ideal and essential cograde
• On the asymptotic cograde of an ideal
• Asymptotic sequences and Rees rings
• Notes on projectively related ideals and residual division
• Asymptotic sequences
• Asymptotic prime divisors and integral extension rings
• Five notes on asymptotic prime divisors
• Essential sequences and Rees rings
• Essential sequences
• Quintasymptotic primes and four results of Schenzel
• Reductions of filtrations
• Prime divisors and divisorial ideals
• On asymptotic prime divisors
• Notes on essentially powers filtrations
• Note on Noetherian filtrations
• On the Chain Problem of Prime Ideals
• Filtrations, closure operations and prime divisors
• U–essential prime divisors and sequences over an ideal
• Note on i-good filtrations and noetherian rees rings
• Rings associated with ideals and analytic spread
• Note on analytic spread and asymptotic sequences

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