The ring of polynomials integral-valued over a finite set of integral elements

DOI10.1216/JCA-2016-8-1-113zbMath1338.13015arXiv1411.1382MaRDI QIDQ262666

Giulio Peruginelli

Publication date: 30 March 2016

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

Full work available at URL: https://arxiv.org/abs/1411.1382

zbMATH Keywords

divided differencesPrüfer ringpullbackinteger-valued polynomialintegral closure

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) 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 (11)

Properly integral polynomials over the ring of integer-valued polynomials on a matrix ring ⋮ Galois structure on integral valued polynomials ⋮ Integer-valued polynomials over matrix rings of number fields ⋮ Transcendental extensions of a valuation domain of rank one ⋮ Some results on the integer-valued polynomials over matrix rings ⋮ Integer-Valued Polynomials on Algebras: A Survey of Recent Results and Open Questions ⋮ Decomposition of integer-valued polynomial algebras ⋮ Non-triviality conditions for integer-valued polynomial rings on algebras ⋮ A note on the Krull dimension of rings between \(D[X\) and \(\mathrm{Int}(D)\)] ⋮ Integer-valued skew polynomials ⋮ Polynomial overrings of \(\mathrm{Int}(\mathbb Z)\)

Cites Work

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• Integral Closure of Rings of Integer-Valued Polynomials on Algebras
• On 𝑃-orderings, rings of integer-valued polynomials, and ultrametric analysis
• Pullbacks of Arithmetical Rings
• Prüfer rings with zero divisors.

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