Integer-valued polynomials on algebras

DOI10.1016/j.jalgebra.2012.10.003zbMath1273.13037arXiv1210.1474OpenAlexW2011958701MaRDI QIDQ2377443

Sophie Frisch

Publication date: 2 July 2013

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

Full work available at URL: https://arxiv.org/abs/1210.1474

zbMATH Keywords

matrix algebraspolynomial ringsKrull dimensionpolynomial mappingsinteger-valued polynomials\(I\)-adic topologytorsion-free algebras

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials in number theory (11C08) Polynomials over commutative rings (13B25) Complete rings, completion (13J10) Matrices, determinants in number theory (11C20)

Related Items (29)

SOME RESULTS ON INTEGER-VALUED POLYNOMIALS OVER MODULES ⋮ Properly integral polynomials over the ring of integer-valued polynomials on a matrix ring ⋮ Integral-valued polynomials over sets of algebraic integers of bounded degree ⋮ Algebraic-integer valued polynomials ⋮ What You Should Know About Integer-Valued Polynomials ⋮ Polynomial functions on upper triangular matrix algebras ⋮ Integer-valued polynomials over matrix rings of number fields ⋮ Integer-Valued Polynomials: Looking for Regular Bases (A Survey) ⋮ Integral Closure of Rings of Integer-Valued Polynomials on Algebras ⋮ Open Problems in Commutative Ring Theory ⋮ Polynomial Dedekind domains with finite residue fields of prime characteristic ⋮ A note on integer-valued skew polynomials ⋮ Generalized rings of integer-valued polynomials ⋮ Some results on the integer-valued polynomials over matrix rings ⋮ 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 ⋮ POLYNOMIALS THAT KILL EACH ELEMENT OF A FINITE RING ⋮ Non-triviality conditions for integer-valued polynomial rings on algebras ⋮ Integer-valued polynomials over subsets of matrix rings ⋮ Integer-valued polynomials on algebras: a survey ⋮ Integer-valued polynomials over block matrix algebras ⋮ A survey on fixed divisors ⋮ Integer-valued skew polynomials ⋮ Split Quaternions and Integer-valued Polynomials ⋮ Multiplicative properties of integer valued polynomials over split-quaternions ⋮ Null ideals of matrices over residue class rings of principal ideal domains

Cites Work

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• Generalized rings of integer-valued polynomials
• The \(n\)-generator property in rings of integer-valued polynomials determined by finite sets
• A sort of polynomial identities of \(M_ n(F)\) with char F\(\neq 0\)
• Interpolation by integer-valued polynomials
• Interpolation domains
• Nullstellensatz and Skolem properties for integer-valued polynomials
• Integer-Valued Polynomials
• Les idéaux premiers de l'anneau des polynomes à valeurs entières.
• A classification of all 𝐷 such that {𝐼𝑛𝑡}(𝐷) is a Prüfer domain
• Integer-Valued Polynomials over Matrix Rings

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