Integer-Valued Polynomials on Algebras: A Survey of Recent Results and Open Questions

DOI10.1007/978-3-319-65874-2_18zbMath1390.13063OpenAlexW2770743792MaRDI QIDQ4639017

Nicholas J. Werner

Publication date: 2 May 2018

Published in: Rings, Polynomials, and Modules (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-65874-2_18

zbMATH Keywords

matrix algebrasregular basisoctonionsinteger-valued polynomialsPrüfer domains\(P\)-orderinginteger-valued rational functions

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Integral closure of commutative rings and ideals (13B22) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials in number theory (11C08) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Power-associative rings (17A05) Research exposition (monographs, survey articles) pertaining to commutative algebra (13-02)

Related Items (7)

SOME RESULTS ON INTEGER-VALUED POLYNOMIALS OVER MODULES ⋮ Null ideals of subsets of matrix rings over fields ⋮ Octonion polynomials with values in a subalgebra ⋮ Integer-valued polynomials over subsets of matrix rings ⋮ Integer-valued polynomials over block matrix algebras ⋮ A survey on fixed divisors ⋮ Irreducibility of integer-valued polynomials I

Cites Work

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• Null ideals of matrices over residue class rings of principal ideal domains
• Polynomial overrings of \(\mathrm{Int}(\mathbb Z)\)
• The ring of polynomials integral-valued over a finite set of integral elements
• Properly integral polynomials over the ring of integer-valued polynomials on a matrix ring
• Galois structure on integral valued polynomials
• Generalized rings of integer-valued polynomials
• The ring of integer valued polynomials on \(2 \times 2\) matrices and its integral closure
• Non-triviality conditions for integer-valued polynomial rings on algebras
• Integer-valued polynomials over quaternion rings.
• Un anneau de Prüfer. (A Prüfer ring)
• On the multiple Nevanlinna-Pick matrix interpolation in the class \(\mathcal C_p\) and the Carathéodory matrix coefficient problem
• Scalar polynomial functions on the \(n\times n\) matrices over a finite field
• The conditions \(\text{Int}(R)\subseteq R_S[X\) and \(\text{Int}(R_S)=\text{Int}(R)_S\) for integer-valued polynomials]
• Wedderburn polynomials over division rings. I.
• Integer valued polynomials on lower triangular integer matrices
• Computing \(J\)-ideals of a matrix over a principal ideal domain
• Integer-valued polynomials on algebras
• Polynomial functions on upper triangular matrix algebras
• Integer-valued polynomials over matrices and divided differences
• Int-decomposable algebras
• Integral-valued polynomials over sets of algebraic integers of bounded degree
• Integer-Valued Polynomials
• Integral Closure of Rings of Integer-Valued Polynomials on Algebras
• On Prüfer domains of polynomials.
• On the Ratios of Integer-Valued Polynomials Over any Algebraic Number Field
• P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.
• A classification of all 𝐷 such that {𝐼𝑛𝑡}(𝐷) is a Prüfer domain
• Fermat's Equation in Real Quaternions
• The octonions
• Integer-valued polynomials on algebras: a survey
• Integer-Valued Polynomials over Matrix Rings
• Integer-Valued Polynomials on the Hurwitz Ring of Integral Quaternions
• Polynomials Inducing the Zero Function on Local Rings
• Split Quaternions and Integer-valued Polynomials
• $P$-orderings of noncommutative rings
• POLYNOMIALS THAT KILL EACH ELEMENT OF A FINITE RING
• Anneaux de 'polynômes à valeurs entières' et anneaux de Fatou
• Polynomes a Valeurs Entieres
• Integer-valued polynomials on commutative rings and modules

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