A classification of the integrally closed rings of polynomials containing \(Z[X]\)

DOI10.1216/JCA-2009-1-1-91zbMath1184.13025MaRDI QIDQ847946

K. Alan Loper, Francesca Tartarone

Publication date: 19 February 2010

Published in: Journal of Commutative Algebra (Search for Journal in Brave)

zbMATH Keywords

valuationPrüferNoetherian

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Integral domains (13G05) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (12)

The Zariski-Riemann Space of Valuation Rings ⋮ A principal ideal theorem for compact sets of rank one valuation rings ⋮ Open Problems in Commutative Ring Theory ⋮ Transcendental extensions of a valuation domain of rank one ⋮ The Quadratic Tree of a Two-Dimensional Regular Local Ring ⋮ Bhargava rings that are Prüfer v-multiplication domains ⋮ On the topology of valuation-theoretic representations of integrally closed domains ⋮ Irredundant intersections of valuation overrings of two-dimensional noetherian domains ⋮ Overrings of two-dimensional noetherian domains representable by noetherian spaces of valuation rings ⋮ Unnamed Item ⋮ Topological Aspects of Irredundant Intersections of Ideals and Valuation Rings ⋮ Integrally closed rings in birational extensions of two-dimensional regular local rings

Cites Work

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• Prüfer v-multiplication domains and the ring \(R[X_{N_ v}\)]
• Topologically defined classes of commutative rings
• On Pruefer v-multiplication domains
• On strong Mori domains
• The valuative tree
• Integer-valued polynomials and Prüfer \(v\)-multiplication domains
• The valuative tree of a two-dimensional regular local ring
• On the uniqueness of the coefficient ring in a polynomial ring
• Integer-Valued Polynomials
• Some questions about pruferv—multiplication domains
• Pairs of Rings with the Same Prime Ideals
• On w-modules over strong mori domains
• Divisorial prime ideals of int(D) when D is a krull-type domain
• Some Results on v-Multiplication Rings
• On Krull Overrings of a Noetherian Domain
• A Construction for Absolute Values in Polynomial Rings

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