The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two

DOI10.4171/RSMUP/62zbMath1472.13006MaRDI QIDQ2039351

Bruce Olberding, William J. Heinzer

Publication date: 2 July 2021

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

zbMATH Keywords

valuation ringalmost Dedekind domainquadratic transformpatch topologyNoetherian local ringcompletely irreducible ideals

Mathematics Subject Classification ID

Structure, classification theorems for modules and ideals in commutative rings (13C05) Ideals and multiplicative ideal theory in commutative rings (13A15) Local rings and semilocal rings (13H99)

Related Items (2)

The Zariski-Riemann Space of Valuation Rings ⋮ The Quadratic Tree of a Two-Dimensional Regular Local Ring

Cites Work

• Unique irredundant intersections of completely irreducible ideals
• Kronecker function rings and abstract Riemann surfaces
• The family of residue fields of a zero-dimensional commutative ring
• PID's with specified residue fields
• A principal ideal theorem for compact sets of rank one valuation rings
• On the topology of valuation-theoretic representations of integrally closed domains
• Noetherian intersections of regular local rings of dimension two
• The tree of quadratic transforms of a regular local ring of dimension two
• Affine schemes and topological closures in the Zariski-Riemann space of valuation rings
• Rational singularities, with applications to algebraic surfaces and unique factorization
• Group-theoretic and topological invariants of completely integrally closed Prüfer domains
• Topological Aspects of Irredundant Intersections of Ideals and Valuation Rings
• The constructible topology on spaces of valuation domains
• Kronecker Function Rings of Transcendental Field Extensions
• Valuations in Function Fields of Surfaces
• On the Valuations Centered in a Local Domain
• Commutative ideal theory without finiteness conditions: Completely irreducible ideals
• Factoring ideals in almost Dedekind domains
• Commutative ideal theory without finiteness conditions: Primal ideals
• Prime Ideal Structure in Commutative Rings
• On Primal Ideals
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