Finitely generated ideals of the ring of integer-valued polynomials

DOI10.1016/0021-8693(83)90213-2zbMath0515.13016OpenAlexW2026862908MaRDI QIDQ1051698

William W. Smith, Robert Gilmer

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0021-8693(83)90213-2

zbMATH Keywords

integer-valued polynomials2-generator propertygenerating sets for finitely generated idealsPruefer domain

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials in number theory (11C08) Polynomials over commutative rings (13B25) Ideals and multiplicative ideal theory in commutative rings (13A15) Commutative rings and modules of finite generation or presentation; number of generators (13E15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items

On ideals in Prüfer domains of polynomials ⋮ On Prüfer non-\(D\)-rings ⋮ Un anneau de Prüfer. (A Prüfer ring) ⋮ What You Should Know About Integer-Valued Polynomials ⋮ Invertible ideals of the ring of integral valued polynomials ⋮ Sets that determine integer-valued polynomials ⋮ Algebraic properties of the ring of integer-valued polynomials on prime numbers ⋮ Direct sums of ideals ⋮ The ring of integer-valued polynomials of a semi-local principal-ideal domain ⋮ Ideals of integer-valued polynomial rings ⋮ Pullbacks of Arithmetical Rings ⋮ The Ring of Integer-Valued Polynomials of a Dedekind Domain ⋮ Prüfer domains of integer-valued polynomials and the two-generator property ⋮ Strongly stable rank and applications to matrix completion ⋮ Generators of maximal ideals in the ring of integer-valued polynomials ⋮ Skolem properties, value-functions, and divisorial ideals ⋮ An Elementary Proof of the Two-Generator Property for the Ring of Integer-Valued Polynomials ⋮ Generating ideals in rings of integer-valued polynomials

Cites Work

• On rings with a certain divisibility property
• Generating ideals in Prüfer domains
• Anneaux de Skolem
• A theorem on ideals in prüfer rings of integral-valued polynomials
• Über die erzeugendenanzahl invertierbarer ideale in prüferringen
• Hilbert rings of integral-valued polynomials
• Ideals in rings of integer valued polynomials.
• A basis for the ring of doubly integer-valued polynomials.
• Les idéaux premiers de l'anneau des polynomes à valeurs entières.
• Polynomes à valeurs entières et propriété de Skolem.
• Anneaux de 'polynômes à valeurs entières' et anneaux de Fatou
• Polynomes a Valeurs Entieres
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