Asymptotic Prime Divisors and Analytic Spreads

DOI10.2307/2043422zbMath0445.13002OpenAlexW4238862972MaRDI QIDQ3889171

Stephen McAdam

Publication date: 1980

Full work available at URL: https://doi.org/10.2307/2043422

zbMATH Keywords

prime divisorsanalytic spreadNoetherian domainaltitude formulaintegral closureAss

Mathematics Subject Classification ID

Commutative Noetherian rings and modules (13E05) Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15)

Related Items

On linear equivalence of the P-adic and P-symbolic topologies ⋮ Symbolic Rees Algebras ⋮ Associated points and integral closure of modules ⋮ On the symbolic topology on an ideal ⋮ On ideals whose adic and symbolic topologies are linearly equivalent ⋮ Symbolic Powers of Prime Ideals and Their Topology ⋮ Stanley depth of the integral closure of monomial ideals ⋮ Note on Asymptotic Prime Divisors, Analytic Spreads and the Altitude Formula ⋮ Analytic spread of filtrations and symbolic algebras ⋮ Analytic spread and non-vanishing of asymptotic depth ⋮ A Note on Asymptotic Prime Sequences ⋮ Associated primes of powers of edge ideals ⋮ Independent elements and asymptotic sequences ⋮ Associated primes and integral closure of Noetherian rings ⋮ An effective avoidance principle for a class of ideals ⋮ Integral closure and generic elements ⋮ Independent elements, unmixedness theorems, and asymptotic prime divisors ⋮ Asymptotic growth of algebras associated to powers of ideals ⋮ On the asymptotic cograde of an ideal ⋮ ANALYTIC SPREAD OF FILTRATIONS ON TWO-DIMENSIONAL NORMAL LOCAL RINGS

Cites Work

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• The asymptotic Ass
• Asymptotic Stability of Ass(M/I n M)
• The asymptotic nature of the analytic spread
• On prime divisors of \(I^n\), \(n\) large