Prüfer domains and rings of integer-valued polynomials

DOI10.1016/0021-8693(90)90233-EzbMath0689.13009OpenAlexW2071634798MaRDI QIDQ581604

Robert Gilmer

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0021-8693(90)90233-e

zbMATH Keywords

Prüfer domainintegral domainalmost Dedekind domainring of integer-valued polynomialsintegers in a finite algebraic number field

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Algebraic numbers; rings of algebraic integers (11R04) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items

Some Boundedness Conditions for Rings of Integer-Valued Polynomials, Compositions of Consistent Systems of Rank One Discrete Valuation Rings, Group-theoretic and topological invariants of completely integrally closed Prüfer domains, Isolated points of the Zariski space, Another Prüfer ring of integer-valued polynomials, 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], The Noetherian Property in Rings of Integer-Valued Polynomials, Bhargava rings that are Prüfer v-multiplication domains, Integer-valued polynomials and Prüfer \(v\)-multiplication domains, Semistar Invertibility on Integral Domains, Projective equivalence of ideals in noetherian integral domains, A note on Itoh (\(\operatorname{e}\))-valuation rings of an ideal, A classification of all 𝐷 such that {𝐼𝑛𝑡}(𝐷) is a Prüfer domain, Integer-valued polynomials on Krull rings, The Ring of Integer-Valued Polynomials of a Dedekind Domain, Prüfer Domains of Integer-Valued Polynomials, Sentences over integral domains and their computational complexities

Cites Work

• Un anneau de Prüfer. (A Prüfer ring)
• The quotient field of an intersection of integral domains
• Integer valued polynomials over a number field
• Semigroup rings as Prüfer rings
• On a class of ideals in an algebraic number field
• Valuation theory
• On Prüfer domains of polynomials.
• An Existence Theorem for Fields with Krull Valuations
• A theorem on ideals in prüfer rings of integral-valued polynomials
• One the existence of fields with few discrete valuations.
• Integral Domains Which are Almost Dedekind
• Anneaux de 'polynômes à valeurs entières' et anneaux de Fatou
• Locally Noetherian Commutative Rings
• Rings With a Finite Number of Primes. I
• Über einen Existenzsatz der Bewertungstheorie
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