A classification of all 𝐷 such that {𝐼𝑛𝑡}(𝐷) is a Prüfer domain

DOI10.1090/S0002-9939-98-04459-1zbMath0887.13010OpenAlexW1564249402MaRDI QIDQ4383043

K. Alan Loper

Publication date: 24 March 1998

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-98-04459-1

zbMATH Keywords

integral domainring of integer-valued polynomialsPrüfer property

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative Noetherian rings and modules (13E05) Polynomials in number theory (11C08) Polynomials over commutative rings (13B25) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (22)

Some Boundedness Conditions for Rings of Integer-Valued Polynomials ⋮ Split absolutely irreducible integer-valued polynomials over discrete valuation domains ⋮ A topological version of Hilbert's Nullstellensatz ⋮ Integer-valued polynomials on algebras ⋮ Pseudo-convergent sequences and Prüfer domains of integer-valued polynomials ⋮ Prüfer intersection of valuation domains of a field of rational functions ⋮ Globalized pseudo-valuation domains of integer-valued polynomials on a subset ⋮ Ultrafilter and Constructible Topologies on Spaces of Valuation Domains ⋮ Sets of lengths of factorizations of integer-valued polynomials on Dedekind domains with finite residue fields ⋮ A principal ideal theorem for compact sets of rank one valuation rings ⋮ Some Closure Operations in Zariski-Riemann Spaces of Valuation Domains: A Survey ⋮ Open Problems in Commutative Ring Theory ⋮ Characterizing absolutely irreducible integer-valued polynomials over discrete valuation domains ⋮ The Patch Topology and the Ultrafilter Topology on the Prime Spectrum of a Commutative Ring ⋮ Interpolation domains ⋮ Integer-valued polynomials and Prüfer \(v\)-multiplication domains ⋮ Integer-Valued Polynomials on Algebras: A Survey of Recent Results and Open Questions ⋮ Prüfer domains of integer-valued polynomials on a subset ⋮ Some applications of the ultrafilter topology on spaces of valuation domains, Part I ⋮ Prüfer domains of integer-valued polynomials and the two-generator property ⋮ Almost Krull domains and their rings of integer-valued polynomials ⋮ Example of an interpolation domain

Cites Work

• Prüfer domains and rings of integer-valued polynomials
• Un anneau de Prüfer. (A Prüfer ring)
• Sequence domains and integer-valued polynomials
• The conditions \(\text{Int}(R)\subseteq R_S[X\) and \(\text{Int}(R_S)=\text{Int}(R)_S\) for integer-valued polynomials]
• Integer-Valued Polynomials, Prufer Domains, and Localization
• On Prüfer domains of polynomials.

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