Generalized rings of integer-valued polynomials

DOI10.1016/j.jnt.2012.05.009zbMath1281.13012OpenAlexW2163630330MaRDI QIDQ452380

Nicholas J. Werner, K. Alan Loper

Publication date: 21 September 2012

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2012.05.009

zbMATH Keywords

Prüfer domaininteger-valued polynomialalgebraic integer

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials in number theory (11C08)

Related Items (26)

Properly integral polynomials over the ring of integer-valued polynomials on a matrix ring ⋮ Integer-valued polynomials on algebras ⋮ Integral-valued polynomials over sets of algebraic integers of bounded degree ⋮ Galois structure on integral valued polynomials ⋮ Algebraic-integer valued polynomials ⋮ Polynomial functions on upper triangular matrix algebras ⋮ Integer-valued polynomials over matrix rings of number fields ⋮ Integral Closure of Rings of Integer-Valued Polynomials on Algebras ⋮ Open Problems in Commutative Ring Theory ⋮ Transcendental extensions of a valuation domain of rank one ⋮ Polynomial Dedekind domains with finite residue fields of prime characteristic ⋮ A note on integer-valued skew polynomials ⋮ The Ring of Integer-Valued Polynomials on 3 × 3 Matrices and Its Integral Closure ⋮ Integer-valued polynomials over matrices and divided differences ⋮ Int-decomposable algebras ⋮ The ring of integer valued polynomials on \(2 \times 2\) matrices and its integral closure ⋮ 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 ⋮ Unnamed Item ⋮ A note on the Krull dimension of rings between \(D[X\) and \(\mathrm{Int}(D)\)] ⋮ Prüfer Domains of Integer-Valued Polynomials ⋮ A survey on fixed divisors ⋮ Integer-valued skew polynomials ⋮ Multiplicative properties of integer valued polynomials over split-quaternions ⋮ Null ideals of matrices over residue class rings of principal ideal domains

Cites Work

• Unnamed Item
• On ideals in Prüfer domains of polynomials
• Un anneau de Prüfer. (A Prüfer ring)
• On rings with a certain divisibility property
• Sequence domains and integer-valued polynomials
• Polynomials. Translated from the second Russian edition by Dimitry Leites.
• Integer-valued polynomials on algebras
• Integer-Valued Polynomials
• A theorem on ideals in prüfer rings of integral-valued polynomials

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