## 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.

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 language | English |
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Pages (from-to) | 559-571 |

Journal | Monatshefte für Mathematik |

Volume | 173 |

DOIs | |

Publication status | Published - 2013 |

## Fields of Expertise

- Advanced Materials Science