The Noetherian Property in Rings of Integer-Valued Polynomials

DOI10.2307/2154451zbMath0780.13009OpenAlexW4243009357MaRDI QIDQ4201533

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

Publication date: 25 August 1993

Full work available at URL: https://doi.org/10.2307/2154451

zbMATH Keywords

integer-valued polynomialsnoetherianness

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative Noetherian rings and modules (13E05) Polynomials over commutative rings (13B25) Integral domains (13G05)

Related Items (7)

The conditions \(\text{Int}(R)\subseteq R_S[X\) and \(\text{Int}(R_S)=\text{Int}(R)_S\) for integer-valued polynomials] ⋮ Integral Closure of Rings of Integer-Valued Polynomials on Algebras ⋮ Strong Mori and Noetherian properties of integer-valued polynomial rings. ⋮ Integer-Valued Polynomials on a Subset ⋮ Almost Krull domains and their rings of integer-valued polynomials ⋮ Interpolation by integer-valued polynomials ⋮ Mori domains of integer-valued polynomials

Cites Work

• Prüfer domains and rings of integer-valued polynomials
• Dimension of an integer valued polynomial ring
• When is an N-ring Noetherian?
• Un anneau de Prüfer. (A Prüfer ring)
• On ideal transforms of Noetherian rings. I
• The Ring of Integer-Valued Polynomials of a Dedekind Domain
• A theorem on ideals in prüfer rings of integral-valued polynomials
• Maximal Ideal Transforms of Noetherian Rings
• Les idéaux premiers de l'anneau des polynomes à valeurs entières.
• On Krull Overrings of a Noetherian Domain
• Fibres formelles d'un anneau local noethérien
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