The topology determined by the symbolic powers of primary ideals

DOI10.1080/00927878508823265zbMath0573.13014OpenAlexW1993919971MaRDI QIDQ3691847

Louis J. jun. Ratliff

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1080/00927878508823265

zbMATH Keywords

primary idealssymbolic powersRees ringintegral extension ringflat extension ringP-adic topologiesP-symbolic topologies

Mathematics Subject Classification ID

Global topological rings (13J20) Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) (54A10) Ideals and multiplicative ideal theory in commutative rings (13A15) Extension theory of commutative rings (13B02) Topological fields, rings, etc. (topological aspects) (54H13)

Related Items (22)

Filtrations, Rees rings, and ideal transforms ⋮ On linearly equivalent ideal topologies ⋮ On linear equivalence of the P-adic and P-symbolic topologies ⋮ On the equivalence of the integral symbolic and adic topologies ⋮ On the relevant transform and the relevant component of an ideal ⋮ On the symbolic topology on an ideal ⋮ On ideals whose adic and symbolic topologies are linearly equivalent ⋮ On the kernel of a monadic transformation ⋮ On quasi-factorial domains ⋮ Locally unmixed modules and linearly equivalent ideal topologies ⋮ Symbolic powers, integral closure and local cohomology ⋮ Note on i-good filtrations and noetherian rees rings ⋮ Symbolic powers of prime ideals with applications to hypersurface rings ⋮ Notes on projectively related ideals and residual division ⋮ Symbolic powers and the associated graded ring ⋮ QUINTESSENTIAL PRIMES AND IDEAL TOPOLOGIES OVER A MODULE ⋮ Integral closures, local cohomology and ideal topologies ⋮ Locally unmixed modules and ideal topologies ⋮ Uniform equivalence of symbolic and adic topologies ⋮ Note on Symbolic Powers and Going Down ⋮ Analytic spread modulo an element and symbolic Rees algebras ⋮ Three Theorems on Form Rings

Cites Work

• On the asymptotic cograde of an ideal
• On linearly equivalent ideal topologies
• New characterizations of quasi-unmixed, unmixed, and Macaulay local domains
• On asymptotic prime divisors
• Prime divisors, analytic spread and filtrations
• Notes on essentially powers filtrations
• Note on asymptotic prime divisors and symbolic powers of primary ideals
• Locally quasi-unmixed Noetherian rings and ideals of the principal class
• A characterization of analytically unramified semi-local rings and applications
• On the finiteness of the derived normal ring of an affine ring
• Symbolic Powers of Prime Ideals and Their Topology
• Asymptotic Factorization of Ideals

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