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Title of Journal: Monatsh Math

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Abbravation: Monatshefte für Mathematik

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Springer Vienna

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DOI

10.1007/978-94-007-2181-4_20

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1436-5081

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Integervalued polynomials over matrices and divid

Authors: Giulio Peruginelli
Publish Date: 2013/06/04
Volume: 173, Issue: 4, Pages: 559-571
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Abstract

Let D be an integrally closed domain with quotient field K and n a positive integer We give a characterization of the polynomials in KX which are integervalued over the set of matrices M nD in terms of their divided differences A necessary and sufficient condition on fin KX to be integervalued over M nD is that for each k less than n the kth divided difference of f is integralvalued on every subset of the roots of any monic polynomial over D of degree n If in addition D has zero Jacobson radical then it is sufficient to check the above conditions on subsets of the roots of monic irreducible polynomials of degree n that is conjugate integral elements of degree n over DI wish to thank Keith Johnson for the useful suggestions I also thank the referee for the several suggestions he/she gave which improved the overall quality of the paper The author was supported by the Austrian Science Foundation FWF Project Number P23245N18

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Other Papers In This Journal:
  1. A central limit theorem for integer partitions
  2. Fully commutative elements in finite and affine Coxeter groups
  3. On semi-rational finite simple groups
  4. On mean values of multiplicative functions on the symmetric group
  5. Simple exceptional groups of Lie type are determined by their character degrees
  6. Löwner chains with complex leading coefficient
  7. On a functional equation related to derivations in prime rings
  8. Ricci solitons and odd-dimensional spheres
  9. Regularity properties of distributions through sequences of functions
  10. An explicit growth condition for middle-degree cuspidal cohomology of arithmetically defined quaternionic hyperbolic n -manifolds
  11. Operations with monotone operators and the monotonicity of the resulting operators
  12. Normal families of meromorphic functions and shared values
  13. Some New Results on the Chu Duality of Discrete Groups
  14. Cauchy integral and singular integral operator over closed Jordan curves
  15. The zero-free region of the derivative of Selberg zeta functions
  16. A note on Engel words of finite groups
  17. Equivalence of plurisubharmonic singularities and Siu-type metrics
  18. Palindromic Prefixes and Diophantine Approximation
  19. Effective uniqueness of Parry measure and exceptional sets in ergodic theory
  20. On matrix valued square integrable positive definite functions
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