Integer valued polynomials on lower triangular integer matrices

DOI10.1007/s00605-013-0481-6zbMath1266.13015OpenAlexW1965299363MaRDI QIDQ1950334

Keith Johnson, Youssef Fares, Sabine Evrard

Publication date: 13 May 2013

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-013-0481-6

zbMATH Keywords

lower triangular matricesdivided differencesinteger valued polynomialspolynomial closure

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials in number theory (11C08) Matrices, determinants in number theory (11C20)

Related Items (23)

Null ideals of subsets of matrix rings over fields ⋮ Properly integral polynomials over the ring of integer-valued polynomials on a matrix ring ⋮ 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 ⋮ A note on integer-valued skew 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 ⋮ Non-triviality conditions for integer-valued polynomial rings on algebras ⋮ Integer-valued polynomials over subsets of matrix rings ⋮ Integer-valued polynomials over block matrix algebras ⋮ A survey on fixed divisors ⋮ Integer-valued skew polynomials ⋮ Split Quaternions and Integer-valued Polynomials ⋮ About Polynomials Whose Divided Differences are Integer-Valued on Prime Numbers ⋮ Null ideals of matrices over residue class rings of principal ideal domains ⋮ The ring of polynomials integral-valued over a finite set of integral elements

Cites Work

• Regular subsets of valued fields and Bhargava's \(v\)-orderings
• Finite differences in finite characteristic
• On 𝑃-orderings, rings of integer-valued polynomials, and ultrametric analysis
• 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>
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