We characterize completely the interpolation domains if D is Noetherian or a Prüfer domain. In the first case, we show that D is an interpolation domain if and only if it is one-dimensional and locally unibranched with finite residue fields; in the second case, if and only if the ring Int(D) of integer-valued polynomials is itself a Prüfer domain.

In general, we show that an interpolation domain must satisfy a double boundedness condition; thus we generalize and simplify Loper's recent characterization of the domains D such that the ring Int(D) of integer-valued polynomials is a Prüfer domain.

1991 Mathematics Subject Classification:

Primary 13B25, 13F05, 13F20; Secondary 13B22, 13B30, 13F30.

PDF: P.-J. Cahen, J.-L. Chabert, S. Frisch, Interpolation domains

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