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- W3100681347 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 $$fin K[X]$$ to be integer-valued over $$M_n(D)$$ is that, for each $$k$$ less than $$n$$ , the $$k$$ th 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 $$D$$ ." @default.
- W3100681347 created "2020-11-23" @default.
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- W3100681347 date "2013-06-04" @default.
- W3100681347 modified "2023-09-26" @default.
- W3100681347 title "Integer-valued polynomials over matrices and divided differences" @default.
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- W3100681347 doi "https://doi.org/10.1007/s00605-013-0519-9" @default.
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