Finite generation properties for various rings of integer-valued polynomials

DOI10.1016/j.jalgebra.2009.04.017zbMath1177.13051OpenAlexW1988255164MaRDI QIDQ731911

Julie Yeramian, Manjul Bhargava, Paul-Jean Cahen

Publication date: 9 October 2009

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2009.04.017

zbMATH Keywords

finite differencesNoetherian ringsDedekind domainsinteger-valued polynomialsvaluation domains

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative Noetherian rings and modules (13E05) Polynomials over commutative rings (13B25) Valuation rings (13F30) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (11)

What You Should Know About Integer-Valued Polynomials ⋮ Integer-Valued Polynomials: Looking for Regular Bases (A Survey) ⋮ The factorial function and generalizations, extended ⋮ Various properties of a general class of integer-valued polynomials ⋮ Paul-Jean Cahen (1946–2019) ⋮ Bhargava rings that are Prüfer v-multiplication domains ⋮ Computing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>r</mml:mi></mml:math>-removed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi></mml:math>-orderings and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi></mml:math>-orderings of order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>h</mml:mi></mml:math> ⋮ An overview of some recent developments on integer-valued polynomials: Answers and Questions ⋮ On 𝑃-orderings, rings of integer-valued polynomials, and ultrametric analysis ⋮ Super-additive sequences and algebras of polynomials ⋮ About Polynomials Whose Divided Differences are Integer-Valued on Prime Numbers

Cites Work

• Integer-Valued Polynomials
• On 𝑃-orderings, rings of integer-valued polynomials, and ultrametric analysis
• Anneaux de Bhargava
• Fonctions $k$-lipschitziennes sur un anneau local et polynômes à valeurs entières
• P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.
• Dérivées et différences divisées à valeurs entières
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