The Ring of Integer-Valued Polynomials of a Dedekind Domain

DOI10.2307/2047787zbMath0694.13009OpenAlexW4231744921MaRDI QIDQ3469202

Robert Gilmer, William W. Smith, David C. Lantz, William J. Heinzer

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2047787

zbMATH Keywords

Dedekind domainPicideal class group of the ring of integer valued polynomials

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials over commutative rings (13B25) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (8)

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 ⋮ Transcendental extensions of a valuation domain of rank one ⋮ Localizations of integer‐valued polynomials and of their Picard group ⋮ Polynomial Dedekind domains with finite residue fields of prime characteristic ⋮ The ring of integer-valued polynomials of a semi-local principal-ideal domain ⋮ The Picard group of an integer-valued polynomial ring ⋮ Unnamed Item

Cites Work

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• Prüfer domains and rings of integer-valued polynomials
• Finitely generated ideals of the ring of integer-valued polynomials
• Un anneau de Prüfer. (A Prüfer ring)
• Integer valued polynomials over a number field
• On a class of ideals in an algebraic number field
• On Prüfer domains of polynomials.
• A theorem on ideals in prüfer rings of integral-valued polynomials
• Anneaux de 'polynômes à valeurs entières' et anneaux de Fatou
• Polynomes a Valeurs Entieres
• Modules Over Dedekind Rings and Valuation Rings

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