Integer-valued polynomials over matrices and divided differences

Giulio Peruginelli

Research output: Contribution to journalArticlepeer-review

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 K [X] which are integer-valued over the set of matrices M n (D) in terms of their divided differences. A necessary and sufficient condition on f ∈ K [X] to be integer-valued over M n (D) is that, for each k less than n, the kth divided difference of f is integral-valued 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 D.
Original languageEnglish
Pages (from-to)559-571
JournalMonatshefte für Mathematik
Volume173
DOIs
Publication statusPublished - 2013

Fields of Expertise

  • Advanced Materials Science

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